Physics — Mechanical Waves, Sound, Interference
Physics — Mechanical Waves, Sound, Interference. Practice questions to deepen understanding of mechanical waves, sound, and interference. Online physics practice with full solutions and step-by-step explanations.
Physics mechanical waves and sound practice — 50 questions: longitudinal/transverse waves, parameters, interference, standing waves, Doppler effect, sonar. Acoustics.
Part A: Introduction to waves (1–12):
- What a wave is
Question 1
2.00 pts
🌊 What is a wave?
What is the definition?
Explanation:
💡 Detailed explanation:
What is a wave? 🌊
🌊 Wave definition: A disturbance that propagates in space and transfers energy without transferring matter 🔍 Components of the definition: 1️⃣ Disturbance: A temporary change in state • water height • air density • rope tension • electric/magnetic field 2️⃣ Propagates in space: The disturbance moves from place to place at a certain speed (v) 3️⃣ Transfers energy: The wave carries energy from point to point but! 4️⃣ Without transferring matter: Very important! The particles do not move with the wave they only oscillate in place The wave passes, the matter remains 💡 Examples: • Wave in water: water does not flow forward • Wave on a rope: the rope does not move • Sound: air does not flow • Light: there is no matter at all! ⚡ Energy: The wave carries: • kinetic energy (motion) • potential energy (deformation) |
Question 2
2.00 pts
📊 Wave types:
What is the difference between longitudinal and transverse?
Explanation:
💡 Detailed explanation:
Wave types! 📊
🌊 Two main types: 📊 Comparison:
🎵 Longitudinal wave: The particles move back and forth in the direction of wave propagation Sound: air molecules approach and recede creating compressions and rarefactions 🌊 Transverse wave: The particles move up and down (or sideways) perpendicular to the direction of wave propagation Rope: The rope rises and falls but the wave moves to the side ⚠️ Important: Light = transverse wave but does not need a medium! (electromagnetic wave) |
Question 3
2.00 pts
📏 Wave parameters:
What are the quantities that characterize a wave?
Explanation:
💡 Detailed explanation:
Wave parameters! 📏
🌊 5 central parameters: 1️⃣ Amplitude (A): The maximum deviation from the equilibrium position Units: metre (m) Meaning: • wave height • disturbance intensity • related to energy: E ∝ A² 2️⃣ Wavelength (λ): The distance between two points in the same phase (crest to crest, trough to trough) Units: metre (m) Meaning: • "length" of one cycle in space • determines colour (in light) • determines pitch of sound 3️⃣ Frequency (f): Number of cycles per second Units: hertz (Hz) = 1/s Meaning: • how many times the wave "strikes" • determines pitch of sound • determines colour of light 4️⃣ Period (T): The time for one cycle Units: seconds (s) Relation to frequency: T = 1/f 5️⃣ Speed (v): Speed of wave propagation Units: m/s The central relation: v = λ·f or: v = λ/T ⚡ Numerical example: Wave in water: A = 10 cm λ = 2 m f = 0.5 Hz T = 1/f = 2 s v = λf = 2×0.5 = 1 m/s |
Question 4
2.00 pts
⚡ The wave equation:
Why v = λ·f?
Explanation:
💡 Detailed explanation:
v = λf! ⚡
The central formula: v = λ·f or: v = λ/T 🔍 Why is it true? Intuitive understanding: Speed = distance / time In the time of one cycle (T): The wave travels a distance of λ So: v = λ/T but T = 1/f therefore: v = λ/(1/f) = λ·f ✓ Another understanding: In one second: • there are f cycles • each cycle is λ "long" • total distance: f×λ distance per second = speed! v = f·λ ✓ 💡 Examples: Example 1: Sound wave: λ = 0.5 m f = 680 Hz v = 0.5 × 680 v = 340 m/s ✓ (speed of sound in air!) Example 2: Light wave: λ = 500 nm = 5×10⁻⁷ m f = 6×10¹⁴ Hz v = 5×10⁻⁷ × 6×10¹⁴ v = 3×10⁸ m/s ✓ (speed of light!) ⚠️ Important: v depends on the medium λ and f depend on the source when v changes → λ changes (f is constant!) |
Question 5
2.00 pts
🎸 Wave on a rope:
What does the wave speed depend on?
Explanation:
💡 Detailed explanation:
Wave on a rope! 🎸
Wave speed on a rope: v = √(T/μ) 🔍 The parameters: T - tension (Tension): The force stretching the rope Units: newton (N) Effect: large T → large v tight rope → fast wave μ - linear density: Mass per unit length μ = m/L Units: kg/m Effect: large μ → small v heavy rope → slow wave 💡 Intuition: • Large tension: large restoring force → large v • Large mass: large inertia → small v The ratio T/μ is reasonable! Numerical example: Rope: m = 0.1 kg L = 2 m → μ = 0.1/2 = 0.05 kg/m Tension: T = 20 N v = √(20/0.05) v = √400 v = 20 m/s 🎸 Musical instrument: Guitar: • thin string (small μ) → high pitch • thick string (large μ) → low pitch • high tension → higher Tuning = changing T! |
Question 6
2.00 pts
🧮 Exercise:
Wave: f=50Hz, λ=4m
What is v?
Explanation:
💡 Detailed explanation:
Basic exercise! 🧮
| 📐 Solution: Given: f = 50 Hz λ = 4 m The formula: v = λ·f v = 4 × 50 v = 200 m/s 💡 Understanding: In each second: • 50 cycles pass • each cycle is 4m long • total: 50×4 = 200m → speed = 200 m/s Simple! |
Question 7
2.00 pts
⚡ Wave types:
What is the difference between mechanical and electromagnetic waves?
Explanation:
💡 Detailed explanation:
Two types! ⚡
📊 Comparison:
🌊 Mechanical waves: Need a medium! • air for sound • water for sea waves • earth for tremors without a medium → no wave therefore: no sound in space! 💡 Electromagnetic waves: Do not need a medium! A changing electric field creates a magnetic field that creates an electric field... continue forever! therefore: light reaches us from the sun through space! ⭐ All: • carry energy • v = λf • characterized by A, λ, f • can interfere, reflect |
Question 8
2.00 pts
➕ Superposition:
What happens when two waves meet?
Explanation:
💡 Detailed explanation:
Superposition principle! ➕
Superposition principle: y_total = y₁ + y₂ The total deviation = sum of the deviations 🔍 What happens? When waves meet: 1️⃣ At the meeting point: the deviations add algebraically 2️⃣ After the meeting: the waves continue as if nothing happened! There is no real "collision" 💡 Examples: Constructive addition: Two waves in the same direction: y₁ = +2 cm y₂ = +3 cm y_total = 2 + 3 = +5 cm Larger amplitude! stronger wave Destructive addition: Waves in opposite directions: y₁ = +2 cm y₂ = -2 cm y_total = 2 + (-2) = 0 cancel out! a moment of silence Partial addition: y₁ = +3 cm y₂ = -1 cm y_total = 3 + (-1) = +2 cm difference ⚠️ Important: • The waves are not damaged • After the meeting they part • continue as usual • not like balls! |
Question 9
2.00 pts
🎭 Interference:
What is the difference between constructive and destructive?
Explanation:
💡 Detailed explanation:
Interference! 🎭
🎭 Interference: The result of superposition of waves 📊 Two types: ✅ Constructive interference: Condition: waves in the same phase (crest+crest or trough+trough) Result: A_total = A₁ + A₂ reinforcement! Path difference: Δx = nλ (n = 0, 1, 2, 3...) integer multiple of λ ❌ Destructive interference: Condition: waves in opposite phases (crest+trough) Result: A_total = |A₁ - A₂| if A₁=A₂ → complete cancellation! Path difference: Δx = (n+½)λ (n = 0, 1, 2, 3...) multiple of half λ 💡 Example: Two speakers: f = 170 Hz v = 340 m/s λ = v/f = 2 m Point at distances: d₁ = 10 m d₂ = 12 m Difference: Δx = 2 m = 1λ → constructive interference! → strong sound If Δx = 1 m = 0.5λ → destructive interference → silence! 🎵 Uses: • acoustics in buildings • noise cancellation • noise-cancelling headphones |
Question 10
2.00 pts
↩️ Reflection:
What happens when a wave meets a boundary?
Explanation:
💡 Detailed explanation:
Reflection! ↩️
| 🔍 What happens at the boundary? A wave meets a boundary: Part of the energy: • reflected (reflection) • transmitted (transmission) • absorbed (absorption) The distribution depends on the media! 💡 Types of reflection: 1️⃣ Fixed end (rigid): Rope tied to a wall Wave reflected inverted! (crest → trough) Phase difference: 180° 2️⃣ Free end (loose): Rope free to move Wave reflected identical! (crest → crest) No phase change 3️⃣ Transition between media: Light rope → heavy rope Part is reflected inverted part passes onward v changes, f is constant → λ changes! 🔊 Sound: Echo = reflection of sound Hits a wall → returns Heard twice! |
Question 11
2.00 pts
🎸 Standing waves:
What is it?
Explanation:
💡 Detailed explanation:
Standing waves! 🎸
Standing wave: A wave pattern that appears as if it is standing still created by interference of a wave with its reflection 🔍 How is it formed? The process: 1️⃣ Wave moves to the right → 2️⃣ Hits a wall and is reflected ← 3️⃣ Outgoing and returning waves interfere 4️⃣ constant interference! → standing pattern 💡 Properties: Nodes: Points always at rest A = 0 Complete destructive interference Distance between nodes: λ/2 Antinodes: Points with maximum oscillation A = maximum Complete constructive interference Distance between antinodes: λ/2 Distance node-antinode: λ/4 🎸 Stretched rope: Two fixed ends: L = n·(λ/2) n = 1, 2, 3... Length = integer multiple of half wavelengths Allowed frequencies: f_n = n·(v/(2L)) f₁ = v/(2L) - fundamental f₂ = 2f₁ - 2nd harmonic f₃ = 3f₁ - 3rd harmonic |
Question 12
2.00 pts
📚 Introduction summary:
What are the central points?
Explanation:
💡 Detailed explanation:
Summary of part A! 📚
🌊 Wave introduction summary: ✅ What we have learned: • Definition: a disturbance that propagates transfers energy without matter • Types: longitudinal vs transverse mechanical vs electromagnetic • Parameters: A, λ, f, T, v • The formula: v = λf • Wave on a rope: v = √(T/μ) • Superposition: y = y₁ + y₂ • Interference: constructive/destructive • Reflection: fixed/free end • Standing waves: nodes and antinodes |
Question 13
2.00 pts
🔊 Sound:
What is it?
Explanation:
💡 Detailed explanation:
What is sound? 🔊
🔊 Sound: A mechanical longitudinal wave of compressions and rarefactions in a medium 🔍 How is it formed? The process: 1️⃣ Vibrating source (voice, string, speaker) 2️⃣ Pushes air molecules → compression 3️⃣ Pulls back → rarefaction 4️⃣ Process repeats → a wave of density! 💡 Properties: • Longitudinal wave: Molecules move back and forth in the direction of wave propagation • Mechanical wave: Needs a medium! No sound in empty space • Media: Air, water, solids Not vacuum Human frequency range: 20 Hz - 20,000 Hz Below: infrasonic Above: ultrasonic Dogs hear up to 45 kHz Bats up to 100 kHz! 🎵 Music vs noise: Music: Constant, defined frequencies periodic waves Noise: Random frequencies non-periodic waves |
Question 14
2.00 pts
⚡ Speed of sound:
What is v in air?
Explanation:
💡 Detailed explanation:
Speed of sound! ⚡
Speed of sound: v ≈ 343 m/s in air at 20°C 📊 In different media:
💡 Trends: solid > liquid > gas Why? Molecules closer together → stronger forces → higher speed Temperature dependence: v ≈ 331 + 0.6T T in Celsius warmer → faster 20°C: v = 331 + 12 = 343 m/s ⚠️ Important: • v does not depend on frequency! • all frequencies at the same speed • it is a property of the medium Comparison to light: Light: 3×10⁸ m/s Sound: 343 m/s Light is almost a million times faster! |
Question 15
2.00 pts
🎵 Pitch:
What does it depend on?
Explanation:
💡 Detailed explanation:
Pitch! 🎵
Pitch: depends on frequency! high f → high pitch low f → low pitch 🎵 Examples:
🎸 Musical instruments: How is the pitch changed? • Shorter string → high f • Thinner string → high f • Higher tension → high f Formula: f = (1/2L)√(T/μ) L = string length T = tension μ = density 🎺 Wind instruments: The length of the air column determines the frequency • Short flute → high • Long saxophone → low f = v/(2L) or v/(4L) (depends on the ends) 💡 Octave: Doubling the frequency = an octave C₁: 262 Hz C₂: 524 Hz ×2 in frequency = "identical" but higher note |
Question 16
2.00 pts
📢 Sound intensity:
What does it depend on?
Explanation:
💡 Detailed explanation:
Sound intensity! 📢
Sound intensity (Loudness): depends on amplitude! large A → loud small A → quiet 📊 Intensity and energy: Relation to energy: I ∝ A² I = intensity (Intensity) energy per area per time Units: W/m² Doubling A → Multiplies I by 4! 🔊 Decibel (dB): A logarithmic measurement unit Formula: L = 10·log₁₀(I/I₀) I₀ = 10⁻¹² W/m² (threshold of hearing) Why logarithmic? Enormous range of intensities! From threshold of hearing to pain: a factor of 10¹² ! In decibels: 0-120 dB more convenient 📊 Decibel scale:
⚠️ Danger: Above 85 dB for a long time → damage to hearing! Above 120 dB → pain and immediate danger |
Question 17
2.00 pts
🎨 Timbre:
What is it?
Explanation:
💡 Detailed explanation:
Timbre! 🎨
Timbre: "colour" of sound What causes different instruments to sound differently at the same note 🔍 What determines it? Harmonics: Every sound = sum of frequencies! • Fundamental frequency (f₁) the lowest frequency • Harmonics f₂ = 2f₁ f₃ = 3f₁ f₄ = 4f₁ ... The ratio between the intensities of the different harmonics → determines the timbre! 🎸 Example: Middle C (262 Hz) Guitar: • f₁ = 262 Hz (strong) • f₂ = 524 Hz (medium) • f₃ = 786 Hz (weak) • High harmonics strong → "bright" sound Flute: • f₁ = 262 Hz (very strong) • f₂ = 524 Hz (very weak) • High harmonics almost zero → "round", "soft" sound 💡 Why is it important? This is what allows us to distinguish between musical instruments! Same note in pitch and intensity but a completely different sound |
Question 18
2.00 pts
↩️ Echo:
What is it?
Explanation:
💡 Detailed explanation:
Echo! ↩️
Echo: Reflection of sound from a surface The original sound is heard and then the reflection 🔍 Conditions for an echo: Minimum distance: The ear distinguishes between two sounds if the time difference is ≥ 0.1 s Sound goes and returns: double distance = 2d time: t = 2d/v t ≥ 0.1 s 2d/343 ≥ 0.1 2d ≥ 34.3 d ≥ 17 m need to be at least 17 metres from the wall! 💡 Distance calculation: Example: Shouting near a mountain Echo heard after 2 s v = 343 m/s Round-trip distance: 2d = v·t = 343×2 = 686 m Distance to the mountain: d = 343 m 🦇 Uses: • Bats and sonar: send ultrasonic measure return time → calculate distance • Sea depth measurement • Pregnancy - ultrasound • Radar (radar) |
Question 19
2.00 pts
🧮 Echo exercise:
Shouting and hearing an echo after 4s
v=340 m/s
What is the distance to the wall?
Explanation:
💡 Detailed explanation:
Echo exercise! 🧮
| 📐 Solution: Given: t = 4 s v = 340 m/s Stage 1: total distance The sound went and returned Round-trip distance: 2d = v·t 2d = 340 × 4 2d = 1360 m Stage 2: distance to the wall d = 1360/2 d = 680 m 💡 Remember: The sound goes to the wall and returns! So we need to divide by 2 |
Question 20
2.00 pts
🎵 Beats:
What is it?
Explanation:
💡 Detailed explanation:
Beats! 🎵
Beats: Oscillations in sound intensity when two sounds at close frequencies are played together 🔍 How does it happen? Interference: Two waves: f₁ = 440 Hz f₂ = 443 Hz Sometimes in the same phase → constructive interference → loud Sometimes in opposite phases → destructive interference → quiet The result: loud-quiet-loud-quiet... Beat frequency: f_beat = |f₁ - f₂| Example: f₁ = 440 Hz f₂ = 443 Hz f_beat = |440 - 443| = 3 Hz → 3 "beats" per second → loud-quiet-loud (3 times per second) 🎸 Use for tuning: Play a known note (440 Hz) and the string we want to tune Hear beats? → The string is not tuned! Tune until the beats disappear → identical frequencies! Example: Hear 5 beats per second Note: 440 Hz The string can be: • 445 Hz (too high) • 435 Hz (too low) Need to try! ⚠️ Note: Beats are heard only when the frequencies are very close (difference smaller than about 10 Hz) Large difference → simply two sounds |
Question 21
2.00 pts
🔬 Ultrasound:
What is it?
Explanation:
💡 Detailed explanation:
Ultrasound! 🔬
Ultrasound: Sound waves above 20,000 Hz Above the human hearing range 📊 Frequency scale:
💡 Uses: 🏥 Medicine: • Pregnancy ultrasound frequency: 2-10 MHz see the fetus • Medical imaging heart, kidneys, liver • Kidney stone shattering (Lithotripsy) • Dental cleaning 🏭 Industry: • Precision cleaning jewellery, watches • Non-destructive testing cracks in materials • Distance measurement sensors 🦇 In nature: • Bats up to 100 kHz echolocation • Dolphins up to 150 kHz navigation and communication • Dogs hear up to 45 kHz (dog whistles!) ⚡ Advantages: • High frequency → small λ → good resolution • Safe (not ionizing radiation) • Non-invasive |
Question 22
2.00 pts
🌍 Infrasound:
What is it?
Explanation:
💡 Detailed explanation:
Infrasound! 🌍
Infrasound: Sound waves below 20 Hz Below the human hearing range 💡 Natural sources: 🌍 Geological: • Earthquakes very low frequencies • Volcanic eruptions • Avalanches • Ocean waves 🌪️ Atmospheric: • Strong wind • Thunderstorms • Cyclones 🐘 Animals: • Elephants communication at 14-24 Hz audible for kilometres! • Whales up to 10 Hz • Giraffes 📡 Uses: • Earthquake detection before humans feel them • Volcanic eruption monitoring • Nuclear test monitoring • Atmospheric research ⚠️ Effects: Although not audible strong infrasound can: • cause discomfort • anxiety • nausea • body vibrations |
Question 23
2.00 pts
🎺 Standing waves in a pipe:
What are the allowed frequencies?
Explanation:
💡 Detailed explanation:
Standing waves in a pipe! 🎺
| 🎺 3 cases: 1️⃣ Both ends open: (flute, recorder) Condition: antinode at each end L = n·(λ/2) n = 1, 2, 3... Frequencies: f_n = n·v/(2L) f₁ = v/(2L) - fundamental f₂ = 2f₁ f₃ = 3f₁ All harmonics! 2️⃣ Both ends closed: (qualitatively rare) Condition: node at each end L = n·(λ/2) n = 1, 2, 3... Frequencies: f_n = n·v/(2L) identical to case 1! 3️⃣ One end closed: (bottle, clarinet) Condition: node at the closed end, antinode at the open end L = n·(λ/4) n = 1, 3, 5, 7... (odd only!) Frequencies: f_n = n·v/(4L) f₁ = v/(4L) - fundamental f₃ = 3f₁ f₅ = 5f₁ Only odd harmonics! 💡 Example: Pipe L=0.5m open on both sides v=340 m/s f₁ = 340/(2×0.5) = 340 Hz f₂ = 680 Hz f₃ = 1020 Hz If closed on one side: f₁ = 340/(4×0.5) = 170 Hz f₃ = 510 Hz f₅ = 850 Hz |
Question 24
2.00 pts
📳 Resonance:
What is it?
Explanation:
💡 Detailed explanation:
Resonance! 📳
Resonance: Enormous reinforcement when a system is forced at its natural frequency 🔍 What happens? Condition for resonance: f_external = f_natural The external (driving) frequency equals the natural (intrinsic) frequency → amplitude grows enormously! → tremendous reinforcement! 💡 Examples: 🎸 Guitar: Play a string The body of the guitar resonates → sound is reinforced Without the body: very weak With the body: strong! 🍷 Glass shattering: A singer sings at the exact frequency of the glass The glass resonates amplitude grows → shatters! 🌉 Tacoma Bridge: A famous bridge that collapsed in 1940 Wind created oscillations at the natural frequency → resonance → huge amplitude → collapse! ⚠️ Danger: Resonance can be dangerous! • bridges • buildings • aeroplanes • machines Need to avoid resonant frequencies in mechanical design! |
Question 25
2.00 pts
📚 Sound summary:
What are the central points?
Explanation:
💡 Detailed explanation:
Sound summary! 📚
🔊 Sound summary: ✅ What we have learned: • Definition: mechanical longitudinal wave compressions and rarefactions • Speed: v≈343 m/s (air) depends on medium and temperature • Pitch: depends on frequency high f → high pitch • Intensity: depends on amplitude large A → loud (dB) • Timbre: sound colour depends on harmonics • Echo: reflection, d≥17m • Beats: f_beat=|f₁-f₂| • Ultrasound: >20kHz • Infrasound: <20Hz • Standing waves: in pipes • Resonance: reinforcement |
Question 26
2.00 pts
🚗 Doppler effect:
What is it?
Explanation:
💡 Detailed explanation:
Doppler effect! 🚗
Doppler effect: Change in observed frequency due to relative motion between source and observer 🔍 How does it happen? Source approaching: The sound waves are "compressed" smaller λ → higher f Higher pitch! ↗️ Example: Ambulance approaching → high pitch Source receding: The sound waves are "stretched" larger λ → lower f Lower pitch! ↘️ Example: Ambulance receding → low pitch 💡 The experience: Ambulance passing by: 🚑→ wheeeeee (high) →🚑 wooooooo (low) The change happens at the moment of passing! ⚠️ Important: • The actual frequency does not change! • Only what the observer hears • Depends on relative speed • Also happens with light! (red shift) 🌟 Applications: • Speed radar (police) • Star speed measurement • Medical ultrasound • Weather forecasting |
Question 27
2.00 pts
📐 Doppler formula:
What is the formula?
Explanation:
💡 Detailed explanation:
Doppler formula! 📐
Doppler formula: f' = f·(v±v_o)/(v∓v_s) 🔍 The signs: Numerator (v±v_o): Observer: • approaching the source: + (f rises) • receding from the source: - (f falls) Denominator (v∓v_s): Source: • approaching the observer: - (f rises) • receding from the observer: + (f falls) 💡 Memory aid: Rule of thumb: Approaching → f rises Observer approaching: + in numerator Source approaching: - in denominator Receding → f falls Observer receding: - in numerator Source receding: + in denominator 📊 Simple example: Ambulance v_s=30 m/s approaching Observer at rest v_o=0 f=500 Hz, v=340 m/s f' = 500·(340+0)/(340-30) f' = 500·340/310 f' = 500·1.097 f' ≈ 548 Hz Increase of ~48 Hz! When receding: f' = 500·340/370 f' ≈ 459 Hz Decrease of ~41 Hz! |
Question 28
2.00 pts
🧮 Doppler exercise:
Train v=25 m/s sounds horn f=600Hz
approaching the station
v_sound=340 m/s
What is the heard frequency?
Explanation:
💡 Detailed explanation:
Doppler exercise! 🧮
| 📐 Solution: Given: f = 600 Hz v_s = 25 m/s (source approaching) v_o = 0 (observer at rest) v = 340 m/s The formula: Source approaching → - in denominator f' = f·(v+v_o)/(v-v_s) f' = 600·(340+0)/(340-25) f' = 600·340/315 f' = 600·1.079 f' ≈ 648 Hz 💡 Understanding: The frequency rose from 600 to 648 Increase of 48 Hz (8%) Higher pitch! When the train recedes: f' = 600·340/365 f' ≈ 559 Hz Decrease! |
Question 29
2.00 pts
🚔 Radar:
How does it work?
Explanation:
💡 Detailed explanation:
Speed radar! 🚔
Speed radar (Radar): Use of the Doppler effect for speed measurement 🔍 How does it work? Stage 1: transmission The radar sends a wave (usually microwave) at a fixed frequency f Stage 2: reflection The wave hits a moving vehicle and is reflected Double Doppler! 1. vehicle = approaching "observer" 2. vehicle = approaching "source" f' = f·(v+v_car)/(v-v_car) (approximation if v_car << v) Stage 3: calculation Δf = f' - f From the frequency difference the speed is calculated! v_car ≈ (Δf/f)·(v/2) very accurate! 💡 Advantages: • immediate measurement • without contact • works from a distance • accurate • can measure several vehicles 🏏 Sport: • baseball ball speed • tennis speed • golf speed Same principle! |
Question 30
2.00 pts
🌌 Doppler in light:
What is the difference from sound?
Explanation:
💡 Detailed explanation:
Doppler in light! 🌌
🌌 Doppler in light: Same principle but with important differences! 🔍 Differences: 1️⃣ Relativistic formula: Speeds close to c need special relativity! Δλ/λ = v/c (for v << c) or more precisely: f'/f = √[(c-v)/(c+v)] 2️⃣ Colour changes: • Blue shift: approaching → small λ bluer light • Red shift: receding → large λ redder light 🌟 In cosmology: The universe is expanding! Almost all galaxies show a red shift → receding from us → the universe is expanding! More distant galaxies → greater speed → greater red shift Hubble''s law: v = H₀·d Speed proportional to distance! ⭐ Applications: • star speed measurement • exoplanet detection (wobble) • measuring the expansion of the universe • dark matter detection This is how we discovered that the universe is expanding! |
Question 31
2.00 pts
💥 Shock waves:
What happens when v_source > v_sound?
Explanation:
💡 Detailed explanation:
Shock waves! 💥
💥 Shock wave: When a source moves faster than sound v_source > v_sound A shock wave is created! 🔍 How is it formed? The process: 1️⃣ Source moves faster than sound 2️⃣ The sound waves cannot "escape" forward 3️⃣ The waves accumulate and form a front 4️⃣ The front = Mach cone (Mach cone) 5️⃣ Cone angle: sin θ = v_sound/v_source ✈️ Sonic boom: What do you hear? A supersonic plane passes Before: silence (faster than sound!) After: BOOM! The sonic boom This is the cone passing over the observer 📊 Mach number: Definition: M = v_object/v_sound • M < 1: subsonic • M = 1: sound barrier • M > 1: supersonic • M > 5: hypersonic Examples: • passenger plane: M ≈ 0.85 • Concorde: M ≈ 2 • F-16: M ≈ 2.5 • missile: M > 5 🌊 Shock waves in water: A fast boat v > v_wave creates a wave cone behind it Same principle! |
Question 32
2.00 pts
🏠 Room resonance:
How does it affect acoustics?
Explanation:
💡 Detailed explanation:
Room resonance! 🏠
🏠 Room resonance: Room = a huge resonance box Certain frequencies are reinforced 🔍 Resonant frequencies: Formula: f = (v/2)·√[(n_x/L_x)² + (n_y/L_y)² + (n_z/L_z)²] n_x, n_y, n_z = 0, 1, 2, 3... L_x, L_y, L_z = room dimensions These frequencies are reinforced! 💡 Example: Room 5m × 4m × 3m: v = 340 m/s Basic resonant frequency (1,0,0): f = 340/(2×5) = 34 Hz Frequency (0,1,0): f = 340/(2×4) = 42.5 Hz Frequency (0,0,1): f = 340/(2×3) = 56.7 Hz and many more... 🎵 Acoustic problems: In a concert hall: • Certain frequencies too strong • Others too weak • "dead points" • Unwanted echo Solutions: • special design • absorbing materials • sound diffusers • non-symmetric dimensions • varying angles 🎸 Recording studio: A serious problem! Need: • acoustic treatment • bass traps • absorbing panels • precise measurements |
Question 33
2.00 pts
🎭 Path difference:
How does it determine interference?
Explanation:
💡 Detailed explanation:
Path difference! 🎭
Path difference: Difference of distances from two sources to a point Determines the type of interference 📊 Conditions: ✅ Constructive interference: Δx = n·λ n = 0, ±1, ±2, ±3... Path difference = integer multiple of λ Waves arrive in phase → reinforce! ❌ Destructive interference: Δx = (n + ½)·λ n = 0, ±1, ±2, ±3... Path difference = half λ, 1.5λ, 2.5λ... Waves arrive out of phase → cancel! 💡 Example: Two speakers: f = 340 Hz v = 340 m/s λ = v/f = 1 m Point at distances: d₁ = 10 m d₂ = 12 m Δx = |12-10| = 2 m = 2λ → constructive! (n=2) → loud sound If d₂ = 10.5 m: Δx = 0.5 m = 0.5λ → destructive! (n=0, half) → silence! 🎵 Application: Acoustics in halls Speaker placement Noise-cancelling headphones |
Question 34
2.00 pts
🌊 Diffraction and scattering:
What is it?
Explanation:
💡 Detailed explanation:
Diffraction and scattering! 🌊
| 🌊 Two phenomena: 1️⃣ Diffraction: A wave hits an obstacle or opening and "bends" around it Examples: • Hearing around corners • Sound through a door • Water waves around a rock Strong condition: The size of the obstacle/opening close to λ Sound: λ ≈ metres → strong diffraction! Light: λ ≈ nanometres → weak diffraction 2️⃣ Scattering: A wave hits a rough surface and scatters in all directions Examples: • Sound in a hall with rough walls • Light from white paper • A cloud scatters light Condition: Irregularity in the surface on the order of λ 💡 Why do we hear around corners? Diffraction! Sound wavelength: 0.5-10 m Door, building corner on this order of magnitude → The sound bends around → Heard even if not direct In contrast: Light: λ ≈ 500 nm → almost no diffraction → Cannot see around corners 🎵 Acoustics: Scattering = good! Helps to spread sound uniformly So in halls: Rough walls Diffuser panels |
Question 35
2.00 pts
🏥 Medical Doppler:
How is it used?
Explanation:
💡 Detailed explanation:
Medical Doppler! 🏥
🏥 Doppler ultrasound: Use of the Doppler effect for measurement of motion in the body 🔍 How does it work? The principle: 1️⃣ Send ultrasound (2-10 MHz) 2️⃣ Reflected from moving blood cells 3️⃣ Frequency changes (Doppler) 4️⃣ From the change calculate flow speed! v_blood = (Δf/f)·(v_sound/2cosθ) θ = measurement angle 💡 Applications: ❤️ Cardiovascular system: • Blood flow examination arteries, veins • Detection of obstructions narrowing • Heart valves function check • Fetal heart rate (Fetal Doppler) 🤰 Pregnancy: • Fetal heart rate from 10 weeks 120-160 beats/minute • Umbilical blood flow health check • Brain blood flow (in special cases) 🧠 Neurology: • Flow to the brain through neck arteries • Stroke detection early obstructions ✅ Advantages: • safe (not radiation) • in real time • non-invasive • relatively inexpensive • portable |
Question 36
2.00 pts
🧮 Comprehensive exercise:
Rope L=2m, v=20 m/s
fixed ends
What is f₃ (third harmonic)?
Explanation:
💡 Detailed explanation:
Standing wave exercise! 🧮
| 📐 Solution: Given: L = 2 m v = 20 m/s Two fixed ends n = 3 (3rd harmonic) The formula: For two fixed ends: f_n = n·v/(2L) f₃ = 3·v/(2L) f₃ = 3·20/(2·2) f₃ = 60/4 f₃ = 15 Hz 💡 Understanding: f₁ = v/(2L) = 20/4 = 5 Hz f₂ = 2f₁ = 10 Hz f₃ = 3f₁ = 15 Hz ✓ In the 3rd harmonic: 3 half wavelengths L = 3λ/2 λ = 4/3 m f = v/λ = 20/(4/3) = 15 Hz ✓ |
Question 37
2.00 pts
📚 Doppler and resonance summary:
What are the central points?
Explanation:
💡 Detailed explanation:
Summary of part C! 📚
🌊 Summary of part C: ✅ What we have learned: • Doppler effect: f'=f(v±v_o)/(v∓v_s) approaching→high, receding→low • Speed radar: use of Doppler • Doppler in light: red/blue shift the universe is expanding • Shock waves: v>v_sound, sonic boom Mach cone, sin θ=v/v_s • Room resonance: resonant frequencies depend on dimensions • Path difference: nλ→constructive, (n+½)λ→destructive • Diffraction and scattering: wave bypasses obstacles • Medical Doppler: blood flow measurement |
Question 38
2.00 pts
🎧 Noise-cancelling headphones:
How does it work?
Explanation:
💡 Detailed explanation:
Noise-cancelling headphones! 🎧
🎧 Active noise cancellation: Use of destructive interference to silence noise! 🔍 How does it work? Stage 1: pickup Microphones in the headphones pick up the external noise For example: aeroplane engine Stage 2: processing The processor creates an exactly inverted wave! If the noise is: y₁ = A·sin(ωt) The processor creates: y₂ = -A·sin(ωt) Phase inverted by 180° Stage 3: cancellation! y_total = y₁ + y₂ y_total = A·sin(ωt) - A·sin(ωt) y_total = 0 Complete destructive interference! → silence! 💡 Effectiveness: Especially effective: • Constant low noises (aeroplane engine, train) • 20-1000 Hz Less effective: • Variable high noises (speech, music) • Above 2000 Hz 🎵 Uses: • long flights • noisy work • focused study • recording studios ⚠️ Note: This is "active cancellation" (Active Noise Cancellation) Different from passive insulation (absorbing materials) |
Question 39
2.00 pts
🐬 Sonar:
How do dolphins and bats "see"?
Explanation:
💡 Detailed explanation:
Biological sonar! 🐬
🐬 Echolocation: "Sight" via sound! 🦇 Bats: How does it work? 1️⃣ Emission: sound 20-100 kHz (ultrasound) through mouth/nose 2️⃣ Reception: huge ears highly sensitive 3️⃣ Analysis: return time → distance intensity → size Doppler → speed frequencies → texture Amazing resolution! Identifies a 1 mm insect! 🐬 Dolphins: An advanced system: 1️⃣ Emission: "clicks" 40-130 kHz through the melon (Melon) a special organ in the forehead 2️⃣ Reception: through the lower jaw! conducts to the inner ear 3️⃣ Capabilities: identifies a 15 cm fish from 110 metres away! sees through sand distinguishes different materials 🚢 Military sonar: Uses: • submarine detection • sea floor mapping • object detection Frequencies: 5-500 kHz ⚠️ Problem: Strong military sonar harms whales and dolphins! causes confusion, injury sometimes death 💡 Comparison: Bat/dolphin are better than any artificial sonar! Evolution of millions of years |
Question 40
2.00 pts
🌍 Earthquakes:
What waves exist?
Explanation:
💡 Detailed explanation:
Seismic waves! 🌍
🌍 Three types of waves: 1️⃣ P waves (Primary): Longitudinal wave • compressions and rarefactions • fastest (6-7 km/s) • travels through solid, liquid, gas • arrives first • relatively minor damage "P" = Primary / Pressure 2️⃣ S waves (Secondary): Transverse wave • perpendicular oscillations • slower (3-4 km/s) • only in solids! (not in liquids) • arrives second • more damage "S" = Secondary / Shear ⚠️ Important: Does not pass through Earth''s outer core (liquid)! 3️⃣ Surface waves: On the surface • Rayleigh waves: elliptical motion like sea waves • Love waves: horizontal motion • slowest • most destructive! • most damage from them 📊 Order of arrival: 1. P waves (fast) 💨 2. S waves (medium) 🌊 3. Surface waves (slow but destructive) 💥 🔬 Seismology: The difference in arrival times allows the calculation of: • distance to the focus • magnitude • exact location |
Question 41
2.00 pts
🌏 Earth''s structure:
How did waves help to discover it?
Explanation:
💡 Detailed explanation:
Earth''s structure! 🌏
🌏 Discovery of Earth''s structure: via seismic waves! We have never drilled deeply (only 12 km) but waves reach the centre! 🔍 The discovery: P waves: ✅ travel through the entire Earth but... • slow down in the outer core • refract • create a "shadow" on the opposite side → indicates a change in speed → a different medium! → probably liquid S waves: ❌ do not pass through the outer core! disappear completely at 103° from the focus → decisive proof: the outer core is liquid! (S waves cannot in a liquid) 🌍 Earth''s structure: The layers (from outside in): 1️⃣ Crust: 5-70 km, solid 2️⃣ Mantle: 2900 km, viscous solid S+P waves pass 3️⃣ Outer core: 2200 km, liquid! only P passes molten iron and copper 4️⃣ Inner core: 1200 km radius, solid! enormous pressure P speeds up again 💡 How did they know? Hundreds of seismic stations around the world measure arrival times and speeds → a 3D map of Earth''s interior! seismic tomography |
Question 42
2.00 pts
🎸 Guitar string:
How is the note changed without tuning?
Explanation:
💡 Detailed explanation:
Guitar physics! 🎸
🎸 Physics of playing: 🔍 The frequency formula: For a string between 2 ends: f = (1/2L)·√(T/μ) L = string length T = tension μ = mass/length 3 ways to change a note! 💡 3 methods: 1️⃣ Fret: Press on the fret → shorten L small L → f rises! For example: L = 65 cm → f₀ L = 32.5 cm → f = 2f₀ (higher octave!) This is the main playing method 2️⃣ Tuning: Tighten/loosen the string → change T large T → f rises This is what is done before playing 3️⃣ String thickness: Thick string → large μ → low f Thin string → small μ → high f So in a guitar: String 1 (thinnest) = highest String 6 (thickest) = lowest 🎵 Intervals: The frets are placed by precise calculation Each fret = a semitone 12 frets = an octave (L halved → f doubled) |
Question 43
2.00 pts
🎭 Hall acoustics:
What is important for good quality?
Explanation:
💡 Detailed explanation:
Hall acoustics! 🎭
🎭 Perfect acoustics: Science and art combined! 🔍 Central factors: 1️⃣ Reverberation time (RT60): The time it takes for the sound to decay by 60 dB Ideal: • speech: 0.5-0.8 s • classical music: 1.5-2.5 s • opera: 1.2-1.8 s • rock: 0.8-1.2 s Depends on the hall size! 2️⃣ Avoiding resonances: Certain resonant frequencies are reinforced too much Solutions: • non-symmetric dimensions • varying angles • varying height • use of bass traps 3️⃣ Uniform diffusion: Every place in the hall needs to hear well Tools: • diffused surfaces • special panels • coffered ceilings • rough walls prevent "dead points" 4️⃣ Controlled absorption: Not too much echo Not too much absorption Materials: • heavy curtains • padded chairs • carpets • absorbing panels A full audience = good absorption! 🌟 Famous halls: Berlin Philharmonic: "vineyard" design stage in the centre audience around perfect acoustics! 💡 Design: A combination of: • engineering • physics • music • architecture A complex and expensive process! |
Question 44
2.00 pts
🧮 Comprehensive exercise:
Radar f=10GHz
vehicle approaching v=30 m/s
c=3×10⁸ m/s
What is Δf?
Explanation:
💡 Detailed explanation:
Electromagnetic Doppler exercise! 🧮
| 📐 Solution: Given: f = 10 GHz = 10¹⁰ Hz v = 30 m/s c = 3×10⁸ m/s Double Doppler: The vehicle "sees" a higher frequency and reflects an even higher frequency Approximation (v << c): Δf/f ≈ 2v/c Δf ≈ 2·(v/c)·f Δf ≈ 2·(30/(3×10⁸))·10¹⁰ Δf ≈ 2·(10⁻⁷)·10¹⁰ Δf ≈ 2·10³ Δf ≈ 2000 Hz 💡 Understanding: Enormous frequency (10 GHz) but the change is relatively small (2 kHz) That is 0.00002% ! but accurately measurable → speed calculation |
Question 45
2.00 pts
📚 Wave formulas:
What are the central formulas?
Explanation:
💡 Detailed explanation:
All the formulas! 📚
🌊 All wave formulas: 📊 Basic formulas:
🎵 Standing waves:
🚗 Doppler effect: General formula: f' = f·(v±v_o)/(v∓v_s) Approaching: f rises Receding: f falls 💥 Shock wave: sin θ = v_sound/v_source M = v/v_sound 🏠 Resonance: f_resonance depends on dimensions RT60 = reverberation time |
Question 46
2.00 pts
⚠️ Common error:
Which claim is wrong?
Explanation:
💡 Detailed explanation:
Common errors! ⚠️
❌ Common errors: ❌ "v depends on frequency" Completely wrong! ✓ v depends only on the medium! All frequencies at the same speed (in the same medium) It is a property of the medium not of the wave! Otherwise we would hear different frequencies at different times ⚠️ Additional errors: ❌ "intensity = frequency" ✓ intensity = amplitude pitch = frequency ❌ "no sound in space because there is no gravity" ✓ no sound because there is no medium (a mechanical wave needs matter) ❌ "S waves pass through liquids" ✓ only solids! (transverse needs rigidity) ❌ "Doppler changes the speed" ✓ Doppler changes only the observed frequency v is constant! ❌ "echo = interference" ✓ echo = reflection interference = superposition ❌ "resonance is always good" ✓ can be dangerous! (Tacoma Bridge) ❌ "ultrasound = loud sound" ✓ ultrasound = high frequency (above 20 kHz) not related to intensity ❌ "a standing wave does not move" ✓ a standing pattern the particles do move! ❌ "interference = cancellation" ✓ can be constructive or destructive ❌ "λ and f depend on each other" ✓ v = λf determines the relation but f is determined by the source v is determined by the medium λ = result |
Question 47
2.00 pts
🎨 Concept map:
What are the central areas?
Explanation:
💡 Detailed explanation:
Concept map! 🎨
🗺️ The full map: Waves 📦 5 areas: 1️⃣ Wave introduction • Definition: a propagating disturbance • Types: longitudinal/transverse • Parameters: A, λ, f, T, v • v = λf • v = √(T/μ) on a rope • Superposition • Constructive/destructive interference • Reflection • Standing waves: nodes and antinodes 2️⃣ Sound • Mechanical longitudinal wave • v ≈ 343 m/s (air) • Pitch = f • Intensity = A (dB) • Timbre = harmonics • Echo: d ≥ 17m • Beats: |f₁-f₂| • Ultrasound >20kHz • Infrasound <20Hz • Standing waves in pipes • Resonance 3️⃣ Doppler effect • Frequency change due to motion • f'=f(v±v_o)/(v∓v_s) • Speed radar • Doppler in light • Red/blue shift • The universe is expanding • Shock waves: v>v_sound • Sonic boom • Mach cone 4️⃣ Advanced resonance • Room resonance • Resonant frequencies • Path difference • Diffraction and scattering • Medical Doppler • Acoustics • Reverberation time 5️⃣ Applications • Noise-cancelling headphones • Biological sonar • Earthquake P/S waves • Earth''s structure • String physics • Hall acoustics |
Question 48
2.00 pts
🔗 Connections:
How is everything related?
Explanation:
💡 Detailed explanation:
The connections! 🔗
🌐 The network of connections: The chain of concepts: Disturbance in a medium ↓ Wave propagates ↓ v = λ·f ↓ Sound = a special case (longitudinal wave in air) ↓ Speed depends on the medium ↓ Motion → Doppler ↓ Interference ↓ Standing waves ↓ Resonance ↓ Practical applications 💡 Additional connections: • v, λ, f are related: v=λf • A → intensity (I∝A²) • f → pitch • Harmonics → timbre • Motion → Doppler • Reflection → echo, standing waves • Interference → beats, noise cancellation • Resonance → strings, rooms • All of this → applications! ⭐ The conclusion: Everything starts from one phenomenon: Wave = a propagating disturbance and from it all of physics flows! |
Question 49
2.00 pts
💻 Technology:
Where are waves used?
Explanation:
💡 Detailed explanation:
Waves in technology! 💻
💻 Waves everywhere! 🌐 Application areas: 🏥 Medicine: • Pregnancy ultrasound • Doppler for blood flow • Lithotripsy (kidney stones) • Physiotherapy • Dental cleaning 🚗 Transport: • Speed radar • Parking sensors • Safety systems • Navigation (radio waves) 🎵 Music: • Musical instruments • Speakers • Microphones • Digital recording • Sound effects 🏗️ Construction: • Hall acoustics • Noise insulation • Non-destructive testing • Seismology 🛡️ Safety: • Alarms • Motion sensors • Noise-cancelling headphones • Earthquake warnings 🌊 Maritime: • Sonar • Sea floor mapping • Fish finding • Underwater communication ⭐ The conclusion: Waves = the basis for modern technology! Almost every device uses waves in some form |
Question 50
2.00 pts
🎓 Summary of exam 156:
What is the central lesson?
Explanation:
💡 Detailed explanation:
Summary of exam 156 - final! 🎓
| 🎉 Exam 156 completed! 🎉 Waves 50 questions | comprehensive perfect coverage 📚 What we learned: 🌊 Part A: Introduction (1-12) • Wave definition: a propagating disturbance • Types: longitudinal/transverse, mechanical/EM • Parameters: A, λ, f, T, v • v = λf - the central formula • Wave on a rope: v=√(T/μ) • Basic exercise • Superposition: y=y₁+y₂ • Constructive/destructive interference • Reflection: fixed/free • Standing waves: nodes and antinodes • Summary Understanding: a wave = a fundamental concept in physics 🔊 Part B: Sound (13-25) • Sound = mechanical longitudinal wave • v≈343 m/s in air • Pitch = frequency (f) • Intensity = amplitude (dB) • Timbre = harmonics • Echo: d≥17m, exercise • Beats: f_beat=|f₁-f₂| • Ultrasound >20kHz • Infrasound <20Hz • Standing waves in pipes • Resonance: reinforcement • Summary Understanding: sound = a special case of waves 🚗 Part C: Doppler (26-37) • Doppler effect: change in f due to motion • Formula: f'=f(v±v_o)/(v∓v_s) • Doppler exercise • Speed radar • Doppler in light: red shift • Shock waves: v>v_sound, boom • Room resonance • Path difference: nλ or (n+½)λ • Diffraction and scattering • Medical Doppler • Standing waves exercise • Summary Understanding: motion changes the observed frequency 💻 Part D: Applications (38-50) • Noise-cancelling headphones • Biological sonar (dolphins/bats) • Earthquakes: P/S waves • Earth''s structure from waves • Guitar string physics • Hall acoustics • Doppler and radar exercise • Full formula table • Common errors • Concept map • Connections • Technological applications • Huge final summary Understanding: waves everywhere in technology 💡 The central lesson: Waves = a fundamental phenomenon! From sound and music through communication and medicine to the structure of planet Earth The same simple principle: a propagating disturbance explains everything! |