📚
WAVE
▢ Disturbance:
❖ Definition: Change in pressure, density or displacement of medium particles about equilibrium position
▢ Wave:
❖ Definition: Disturbance transferred from one part of medium to next with finite velocity due to repeated periodic motion of medium particles about mean position
Table 1: Wave Dimension
Medium / Case | Wave dimension |
|---|---|
Water surface | 2-dimensional |
String | 1-dimensional |
Sound and light | 3-dimensional |
❖ General Points:
- •Wave transfers energy
- •Particle executes SHM about mean position
- •No net permanent transport of medium particles
- •Frequency depends on source, not medium
- •When wave changes medium, frequency remains constant
▢ Types of Wave:
Table 1: Mechanical vs Non-mechanical Wave
Feature | Mechanical / Elastic wave | Non-mechanical / Electromagnetic wave |
|---|---|---|
Medium | Requires material medium | No medium required |
Propagation | Due to elasticity and inertia of medium | Can travel in vacuum |
Examples | Water wave, sound wave, string wave, spring wave, seismic wave | Light, heat radiation, infrared, X-rays, γ-rays, microwaves |
Nature | May be transverse or longitudinal | Always transverse |
❖ Do You Know:
- •Acoustic wave is not electromagnetic wave
- •β-rays do not belong to electromagnetic spectrum
- •All non-mechanical waves are transverse
▢ Transverse Wave:
❖ Definition: Wave in which vibration of particles is perpendicular to direction of propagation
Table 1: Transverse Wave Features
Feature | Answer |
|---|---|
Particle motion | SHM about mean position |
Medium requirement | Rigid medium |
Present in | Solids; not in gases |
Pressure and density | Remain uniform |
Polarisation | Possible |
Transfer | Energy transfer; no mass transport |
Wave form | Crest and trough |
Examples | Wave on stretched string, light wave, heat wave |
▢ Longitudinal Wave:
❖ Definition: Wave in which vibration of particles is parallel to direction of propagation
Table 1: Longitudinal Wave Features
Feature | Answer |
|---|---|
Particle motion | Parallel to wave propagation |
Polarisation | Not possible |
Pressure and density | Change |
Present in | Solids, liquids and gases |
Wave form | Compression and rarefaction |
Examples | Sound wave, wave in long coil/spring |
▢ Mechanical Waves in Different Media:
Table 1: Media and Mechanical Wave Type
Medium | Type of wave |
|---|---|
String under tension | Always transverse |
Gases and liquids | Always longitudinal because they cannot sustain shear |
Solids | Both transverse and longitudinal depending on mode of excitation |
Tuning fork | Prongs transverse; stem longitudinal |
Earthquake rocks | S-waves transverse; P-waves longitudinal |
Water / capillary wave | Combination of longitudinal and transverse; ripple shape elliptical |
▢ Transverse vs Longitudinal Wave:
Table 1: Comparison
Feature | Transverse wave | Longitudinal wave |
|---|---|---|
Particle vibration | Perpendicular to propagation | Parallel to propagation |
Polarisation | Possible | Not possible |
Net displacement over one cycle | Zero | Greater than zero / compression-rarefaction |
Density of medium | Remains constant | Changes |
Transfer | Only energy | Energy and momentum |
Produced in liquid | Only on surface | Inside liquid also |
Propagation form | Crest and trough | Compression and rarefaction |
Pressure change | No pressure change | Pressure changes |
Examples | Stretched string, light wave | Sound wave, spring wave |
▢ Wave Characteristics:
Table 1: Basic Quantities
Quantity | Meaning / Formula |
|---|---|
Displacement | Position of vibrating particle from mean position at an instant |
Amplitude | Maximum displacement from mean position |
Time period | Time for one complete oscillation |
Frequency | Number of oscillations per second |
Frequency relation | f = 1/T |
Angular frequency | ω = 2πf = 2π/T |
Wavelength | Distance travelled by wave in one complete cycle |
Wave velocity | v = fλ = λ/T |
Wave number | k = 2π/λ |
Phase velocity | v = ω/k |
❖ Resultant Amplitude:
Table 1: Two Waves Superposition
Condition | Formula |
|---|---|
General | A = √(a₁² + a₂² + 2a₁a₂ cosφ) |
Maximum amplitude | Amax = a₁ + a₂ when φ = 0° |
Minimum amplitude | Amin = |a₁ - a₂| when φ = 180° |
▢ Phase and Phase Difference:
Table 1: Phase Relations
Condition | Formula |
|---|---|
Phase angle in time | φ = (2π/T)t |
Phase difference for path difference Δx | Δφ = (2π/λ)Δx |
Path difference for 2π phase difference | λ |
Two waves of frequencies f₁ and f₂ | Δφ = 2π(f₂ - f₁)Δt |
Phase at t = 0 | Initial phase / epoch |
▢ Vibrations:
Table 1: Free, Forced, Damped and Resonance
Type | Meaning / Example |
|---|---|
Free vibration | Body vibrates without external force; frequency = natural frequency |
Forced vibration | Body vibrates due to external periodic force |
Resonance | Maximum amplitude when forcing frequency = natural frequency |
Undamped vibration | No energy loss; amplitude remains constant |
Damped vibration | Energy dissipates; amplitude decreases gradually |
Resonance example | Wooden plank vibrating with sound source |
Bridge safety | Soldiers should not march in step on bridge |
Hollow box in sonometer | Increases sound intensity |
Microphone diaphragm | Forced vibration |
Bell material | Metal, not wood, because wood has high damping |
▢ Plane Progressive Wave:
❖ Definition: Wave transferring energy from one part of space to another; particles vibrate successively
❖ Properties:
- •All particles vibrate with same amplitude and same time period
- •All particles pass through equilibrium successively with same speed
- •No particle is permanently at rest
- •At a particular instant, particles lie on sine curve
- •In complete vibration, all particles reach same position simultaneously
Table 1: Progressive Wave Equations
Case | Equation |
|---|---|
General | y = a sin(ωt ± kx + φ₀) |
Along +x direction | y = a sin(ωt - kx) |
Along -x direction | y = a sin(ωt + kx) |
Using f and λ | y = a sin 2π(ft - x/λ) |
Using T and λ | y = a sin 2π(t/T - x/λ) |
Particle velocity | dy/dt = aω cos(ωt - kx) |
Maximum particle velocity | vmax = aω at y = 0 |
Minimum particle velocity | vmin = 0 at y = ±a |
Slope of wave | dy/dx = -ka cos(ωt - kx) |
Particle velocity relation | vparticle = wave velocity × slope of wave |
▢ Velocity of Transverse Mechanical Wave:
Table 1: Transverse Wave Speed
Medium / Condition | Formula |
|---|---|
Stretched string | v = √(T/μ) |
String with cross-section A | v = √(T/ρA) |
Using stress S | v = √(S/ρ) |
Wire with Young modulus Y and strain | v = √(Y × strain / ρ) |
Solid by rigidity modulus η | v = √(η/ρ) |
At distance x from free end of hanging string | v = √(xg) |
❖ Symbols:
- •T = tension
- •μ = mass per unit length
- •ρ = density
- •A = area of cross-section
▢ Velocity of Sound:
❖ General Formula: v = √(E/ρ)
Table 1: Sound Speed Formulae
Medium / Condition | Formula / Value |
|---|---|
Solid rod | v = √(Y/ρ) |
Unbounded solid | v = √((B + 4η/3)/ρ) |
Liquid or gas | v = √(B/ρ) |
Newton formula | v = √(P/ρ) ≈ 280 m/s |
Laplace correction | v = √(γP/ρ) |
Ideal gas | v = √(γRT/M) |
Air at 0°C | v ≈ 331 m/s |
Air at NTP | v ≈ 330–332 m/s |
Temperature relation | v ∝ √T |
Small temperature change | vₜ = v₀(1 + t/546) |
Practical formula | vₜ = (332 + 0.61t) m/s |
Table 2: Velocity of Sound in Different Media
Medium | Speed |
|---|---|
Hydrogen gas | 1296 m/s; maximum among gases |
Air | 330 m/s |
Oxygen gas | 315 m/s; minimum among common gases |
Sea water | 1535 m/s |
Water | 1450 m/s |
Kerosene | 1315 m/s |
Steel | 5200 m/s; maximum among solids |
❖ Speed Order: vsolid > vliquid > vgas
▢ Factors Affecting Velocity of Sound:
Table 1: Effects
Factor | Effect |
|---|---|
Density | v ∝ 1/√ρ |
Temperature | v ∝ √T |
Pressure | No effect at constant temperature |
Humidity | Moist air > dry air because moist air density is lower |
Wind | Along wind: V = Vs + Vw cosθ; against wind: V = Vs - Vw cosθ |
Amplitude | No effect |
Frequency | No effect |
Phase | No effect |
Loudness / pitch / quality | No effect |
Shape | No effect |
❖ Gas Type Order: Monoatomic gas > Diatomic gas > Triatomic gas
▢ Sound in Mixture:
Table 1: Mixture Formulae
Quantity | Formula |
|---|---|
Molecular mass by volume | Mmix = (M₁V₁ + M₂V₂)/(V₁ + V₂) |
Molecular mass by mole | Mmix = (M₁n₁ + M₂n₂)/(n₁ + n₂) |
Density mixture | ρmix = (ρ₁V₁ + ρ₂V₂)/(V₁ + V₂) |
Specific heat ratio | γmix = Cp/Cv |
Velocity | vmix = √(γmix RT/Mmix) |
▢ Displacement and Pressure Waves:
Table 1: Sound Wave Equations
Quantity | Formula / Relation |
|---|---|
Displacement wave | y = a sin(ωt - kx) |
Pressure wave | P = -B(dy/dx) |
Pressure wave | P = aBk cos(ωt - kx) |
Pressure amplitude | P₀ = aBk |
Pressure maximum | At displacement minimum |
Pressure minimum | At displacement maximum |
Pressure at compression | Maximum |
Pressure at rarefaction | Minimum |
▢ Energy Power and Intensity of Wave:
Table 1: Energy and Intensity Formulae
Quantity | Formula |
|---|---|
Energy in small element dx | dE = 2π²n²a²μ dx |
Energy gradient | dE/dx = 2π²n²a²μ |
Power | P = 2π²n²a²μv |
Intensity | I = P/A |
Intensity of sound wave | I = 2π²n²a²ρv |
Pressure-intensity relation | I = P₀²/(2ρv) |
Amplitude relation | I ∝ a² |
Pressure amplitude relation | I ∝ P₀² |
Table 2: Intensity with Distance
Source | Relation |
|---|---|
Point source / spherical wave | I ∝ 1/r², a ∝ 1/r |
Line source / cylindrical wave | I ∝ 1/r, a ∝ 1/√r |
Plane progressive wave | I constant, a constant |
▢ Reverberation:
❖ Definition: Persistence of sound in room/hall due to repeated reflection from walls, floor, ceiling and objects
Table 1: Sabine Formula
Quantity | Formula / Meaning |
|---|---|
Reverberation time | T = KV/AS = 0.18V/ΣSA |
V | Volume of enclosed space |
A | Absorption coefficient |
S | Total area of enclosed space |
Good audibility | Reverberation time nearly 1 sec |
▢ Sound Classification:
Table 1: Frequency Range
Type | Frequency / Wavelength |
|---|---|
Audible sound | 20 Hz to 20,000 Hz |
Infrasonic / subsonic | < 20 Hz; λ > 16.5 m |
Ultrasonic | > 20,000 Hz; λ < 1.65 cm |
❖ Ultrasound Uses:
- •Depth measurement of sea/lakes
- •Bloodless surgery
- •Wave therapy
- •Sonography
❖ Ultrasound Production:
- •Piezoelectric effect
- •Magnetostriction method
- •Galton's whistle
▢ Supersonic and Mach Number:
Table 1: Supersonic Motion
Term | Meaning / Formula |
|---|---|
Supersonic body | Body moving faster than sound |
Shock wave | Destructive wave behind supersonic body |
Mach number | speed of body / speed of sound in air |
Mach number 1 | 330 m/s |
Mach number 2 | 660 m/s |
▢ Echo and Sound Level:
Table 1: Echo and Sound Level
Quantity | Formula / Value |
|---|---|
Echo | Multiple reflection of sound |
Minimum distance for echo | 16.5 m |
Persistence of hearing | 1/10 sec |
Threshold of hearing | I₀ = 10⁻¹² W/m² |
Threshold of pain | 1 W/m² |
Sound level | SL = 10 log(I/I₀) |
Threshold of pain level | 120 dB |
90 dB vs 40 dB | 90 dB is 10⁵ times more intense |
▢ Electromagnetic Wave in Medium:
Table 1: EM Wave Speed
Medium | Formula |
|---|---|
Vacuum | c = 1/√(μ₀ε₀) = 3 × 10⁸ m/s |
Other medium | v = 1/√(με) |
Relation | c/v = √(μrεr) |
▢ Important Read and Digest:
Table 1: One-Line Facts
Fact | Answer |
|---|---|
Sound wave | Longitudinal mechanical wave |
Sound waves do not show | Polarisation |
Speed of sound in gas | Depends on density and elasticity |
Increasing order of wavelength | Cosmic rays < γ-rays < X-rays < UV < visible < IR < microwaves < radio waves |
Sound louder at night | Due to decrease in density |
Out of phase particles distance | λ/2 |
Particle returns to mean after | T/4 |
Sound cannot travel through vacuum | Needs material medium |
Explosion on moon | Cannot be heard on earth |
Ultrasonic waves homogeneous solution | Can produce perfectly homogeneous solutions |
Laplace correction | Needed because sound propagation is adiabatic |
Number of waves per unit length | Wave number |
Q1.
The distance between two points differing in phase by 60° having wave velocity 360 m/s and frequency 500 Hz is
Q2.
Sound travels fastest in
Q3.
Oxygen is 16 times heavier than H₂. Equal volumes of hydrogen and oxygen are mixed. Ratio of velocity of sound in mixture to oxygen is
Q4.
The relation between phase difference and path difference is
Q5.
Phenomenon associated with transverse wave only is
Q6.
The frequency of sound audible to human is
Q7.
The intensity of sound at night increases because of
Q8.
Sound waves in rocks are
Q9.
Velocity of sound in air at STP is 330 m/s. Distance covered in 2 s when temperature is 30°C is nearly
Q10.
If R is radius of a resonance tube, end correction to be applied is
Q11.
If distance between source and cliff is S and velocity of sound is V, time for second echo is
Q12.
Velocity of sound in water is 1400 m/s and density is 1000 kg/m³. Bulk modulus of elasticity of water is
Q13.
Laplace correction in Newton's formula for velocity of sound is needed because sound waves
Q14.
Angle between particle velocity and wave velocity in transverse wave is
Q15.
Intensity of sound gets reduced by 10% after passing through a block. After two such blocks, intensity of outgoing sound is
Q16.
Sound waves travel in a medium whose adiabatic elasticity is E₁ and isothermal elasticity is E₂. Velocity of sound is proportional to
Q17.
A change in temperature affects which property of sound?
Q18.
Which of the following is a mechanical wave?
Q19.
A radio station has a band 30 m. Frequency of electromagnetic wave from the station is
Q20.
Increase in velocity of sound for 1°C rise in air temperature is about
Q21.
If 4 g helium at STP has volume 22.4 L, speed of sound in helium at 0°C and 1 atm is nearly
Q22.
If x = a sin(ωt + π/6) and x' = a cosωt, phase difference between waves is
Q23.
Two sound waves y = a sin(ωt - kx) and y = b cos(ωt - kx) have phase difference
Q24.
Two waves y₁ = a sin(ωt + π/6), y₂ = a cosωt have resultant amplitude
Q25.
Equation of progressive wave y = 4 sin[π + (t/5 - x/9) + π/6] represents
Q26.
If pressure amplitude of a sound wave is tripled, intensity becomes
Q27.
Velocity of sound in air is independent of change in
Q28.
Sound waves having which frequencies are audible to human beings?
Q29.
Temperature at which speed of sound in air becomes double of its value at 27°C is
Q30.
If pressure of air is four times, speed of sound becomes
Q31.
Velocity of sound in hydrogen and oxygen gases at given temperature are in ratio
Q32.
Speed of sound in hydrogen at NTP is 1270 m/s. Speed in mixture of hydrogen and oxygen in ratio 4:1 by volume is
Q33.
One property of sound affected by change in air temperature is
Q34.
Minimum distance of reflecting boundary from source of sound to hear distinct echo is
Q35.
A string of length L and mass M hangs freely. Velocity of transverse wave at distance x from free end is
Q36.
A wave propagating along positive x-axis is y = A sin(ωt - kx). Reflected wave from rigid boundary is
Q37.
Two waves having phase difference 60° have path difference
Q38.
A pulse reaches fixed end of stretched string and is reflected. Reflected pulse has
Q39.
A man standing between two cliffs claps and hears echoes at 1 s interval. If speed of sound is 340 m/s, distance between cliffs is
Q40.
When sound passes from one medium to another, quantity which remains unchanged is
Q41.
Speed of sound is maximum in
Q42.
Two progressive waves y₁ = 0.06 sin 2π(0.04t + 0.1x), y₂ = 0.03 sin 2π(0.08t + 0.2x). Ratio of intensities is
Q43.
Man hears thunder 6 s after lightning. Temperature is 27°C. Distance of flash from him is nearly
Q44.
Man between two cliffs hears echo on third clap when he claps at 4 per second. Speed of sound 320 m/s. Distance between him and obstruction is
Q45.
Velocity of sound in air at STP is 330 m/s. Distance covered in 2 s when temperature is 30°C is
Q46.
Two uniform wires have same length and tension; diameters ratio 1:2. Plucked together, their frequency ratio is
Q47.
Phase difference between y₁ = a sinωt and y₂ = a cosωt is
Q48.
Equation of transverse wave y = 10 sinπ(0.01x - 2t). Frequency is
Q49.
Frequency of radio waves is 15 MHz. Wavelength is
Q50.
Two waves y₁ = 20 sinπθ and y₂ = 40 sin100πθ. Ratio of intensities I₂/I₁ is
Q51.
Sound wave has frequency 500 Hz and velocity 350 m/s. Distance between two particles with phase difference 60° is
Q52.
Equation of progressive wave y = Y₀ sin2π(ft - x/λ). Maximum velocity of particle is
Q53.
Equation of progressive wave is y = 6 cos(1800t - 60x), x in metre. Ratio of maximum particle velocity to wave velocity is
Q54.
Transverse wave is produced in string of length 0.6 m and linear density 0.2 kg/m. Tension is 80 N. If vibrating in 3 segments with amplitude 0.5 cm, velocity amplitude of particle is
Q55.
Distance between two points differing in phase by 60° with velocity 360 m/s and frequency 500 Hz is
Q56.
A simple harmonic wave equation y = 10 sin(2πt/T + φ), if T = 30 s and y = 5 cm at t = 0, phase angle at t = 7.5 s is
Q57.
Speed of sound in H₂ at NTP is 1270 m/s. Speed in mixture of H₂ and O₂ in ratio 4:1 by volume is
Q58.
Speed of sound is more in
Q59.
String of length L stretched by L/20 has transverse wave speed v. If stretched by L/10, speed becomes
Q60.
Uniform copper wire fixed at both ends, tension negligible. Speed of transverse wave at 10°C is
Q61.
Transverse wave in string of length 20 m and mass 5 g has speed 10 m/s. Time taken by transverse wave to reach middle of string is
Q62.
Linear density of vibrating string is 10⁻⁴ kg/m. Transverse wave equation y = 0.25 sin(x + 30t). Tension in string is
Q63.
Young's modulus of material of rod is 2 × 10¹¹ N/m² and density is 8000 kg/m³. Time taken by sound wave to cross 1 m is
Q64.
Ship sends longitudinal wave to sea bottom and wave returns from 2 s. Bulk modulus 2.3 × 10⁹ N/m² and density 1 g/cc. Sea depth is
Q65.
If temperature is raised by 1°C from 300 K, percentage change in speed of sound in air is
Q66.
Amplitude of wave at 10 cm is A. Amplitude at 40 cm is
Q67.
Source of sound emits sound equally in all directions in non-absorbing medium. For points at 9 m and 25 m, ratio of amplitudes is
Q68.
If pressure amplitude of wave increases by 1%, intensity
Q69.
Intensity of sound in air for density 1.3 kg/m³, v = 330 m/s and pressure 1.01 × 10⁵ N/m² is
Q70.
Equation of wave pulse y = 10/[5 + (x + 3t)²], x,y in cm and t in s. Second moment displacement is
Q71.
Equation of wave pulse y = 1/[2 + (x + 2t)²], x,y in cm and t in s. Velocity of wave is
Q72.
Equation of wave pulse y = 0.8/[5 + (4x + 5t)²]. Wave pulse is travelling toward
Q73.
Displacement of wave pulse is y = 1/(1+x²) at t = 0 and y = 1/[1+(x-1)²] at t = 2 s. Velocity after 2 s is
Q74.
Ratio of velocity of sound in hydrogen gas (γ = 7/5) to helium gas (γ = 5/3) at same temperature is
Q75.
A man on ground hears jet sound at angle 30° with vertical. If speed of sound is v, speed of jet is
Q76.
In ripple tank, one pulse every tenth second and distance between consecutive pulses is 30 mm. If pulses are produced at half-second intervals, new distance is
Q77.
A wave of frequency 1000 Hz travels between X and Y, distance 600 m in 2 s. Number of wavelengths in distance XY is
Q78.
Cloud elevation 60° above horizon. Thunder heard 8 s after lightning. Speed of sound 300 m/s. Vertical height of cloud is
Q79.
A sings note and B sings note with exactly 1/8 frequency of A. Energies of sound are equal. Output amplitude of B is
Q80.
Velocity of sound in ideal gas at temperatures T₁ and T₂ are V₁ and V₂. Relation is
Q81.
Two light waves of same frequency and displacement are represented by diagram. Phase difference between waves is
Q82.
Two wires of same length, tension and diameter with density ratio 1:3 have frequency ratio
Q83.
Young's modulus of steel is 2 × 10¹¹ N/m² and density 78 × 10² kg/m³. Velocity of sound in steel is
Q1.
The distance in between 2 points differing in phase by 60° having wave velocity 360 m/s and frequency of wave 500 Hz is:
📅BP 2013•BP 2012
Q2.
Sound travels fastest in
Q3.
Oxygen is 16 times heavier than H₂. Equal volumes of hydrogen and oxygen are mixed, the ratio of velocity of sound in mixture to O₂ is
📅BP 2012
Q4.
The relation between phase difference and path difference is
📅BP 2011
Q5.
Phenomenon associated with transverse wave only is
📅BP 2010
Q6.
The frequency of sound audible to humans is
📅BP 2010
Q7.
The intensity of sound at night increases because of:
📅IOM 2013
Q8.
Sound waves in rocks are
📅IOM 2009
Q9.
Velocity of sound in air at STP is 330 m/s. The distance covered by sound in 2 seconds when atmospheric temperature is 30°C will be:
📅MOE 2013
Q10.
If R is the radius of a resonance tube, the end correction to be applied is
📅MOE 2013
Q11.
If distance between source of sound and a cliff is s. If the velocity of sound is V, the time taken to hear the 2nd echo is
📅MOE 2012
Q12.
The velocity of sound in water is 1400 m/s. The density of water is 1000 kg/m³. Bulk modulus of elasticity of water is
📅MOE 2012
Q13.
Laplace's correction in the expression for velocity of sound is needed because sound waves
📅MOE 2010
Q14.
Angle between particle and wave velocity in transverse wave is:
📅MOE 2010
Q15.
The intensity of sound gets reduced by 10% on passing through a block. If it passes through two such blocks, then intensity of outgoing sound is:
📅MOE 2009
Q16.
Sound waves are travelling in a medium whose adiabatic elasticity is Eₐ and isothermal elasticity is Eᵢ. The velocity of sound is proportional to
📅MOE 2009
Q17.
A change in temperature affects which property of sound?
📅KU 2014
Q18.
Which of the following is a mechanical wave?
📅KU 2012
Q19.
A radio station has a band of 30 m. The frequency of electromagnetic waves from this station will be:
📅IOM 2012
Q20.
The increase in velocity of sound for 10°C rise of temperature is (v₀ = 332 m/s)
Q21.
If 4 g of Helium under STP has a volume of 22.4 litre, the speed of sound waves in an atmosphere of Helium at 0°C and 1 atm pressure is
Q22.
If x = a sin(ωt + π/6) and x' = a cosωt, then what is the phase difference between the two waves
Q23.
Two sound waves are given by y = a sin(ωt - kx) and y' = b cos(ωt - kx). The phase difference between the two waves is
Q24.
Two waves are represented by y₁ = a sin(ωt + π/6) and y₂ = a cosωt. Their resultant amplitude is
Q25.
Equation of progressive wave is given by y = 4 sin[π(t/5 - x/3) + π/6]. Which is correct?
Q26.
If the pressure amplitude in a sound wave is tripled, then by what factor the intensity of the sound wave is increased
Q27.
The velocity of sound in air is independent of change in
📅IOM 2001
Q28.
Sound waves having which frequency are audible to humans?
Q29.
The temperature at which the speed of sound in air becomes double of its value at 27°C is
Q30.
The speed of sound in air at NTP is 300 m/s. If air pressure becomes four times, then the speed will be
Q31.
Velocity of sound is measured in hydrogen and oxygen gases at given temperature. The ratio (V_H/V_O) will be
Q32.
The speed of sound in hydrogen at NTP is 1270 m/s. Speed in a mixture of H₂ and O₂ (4:1 by volume) will be
Q33.
What must be the minimum distance of reflecting boundary to hear distinct echo? (v = 330 m/s)
Q34.
A string of length 'L' and mass 'M' hangs freely. The velocity at distance 'x' from free end is
Q35.
A wave y = A sin(ωt - kx) reflected from rigid boundary becomes
Q36.
Two sound waves with 60° phase difference have path difference of
Q37.
A pulse reaching fixed end reflects with
Q38.
A man between two cliffs hears echoes at 1s intervals (v = 340 m/s). Distance between cliffs is
Q39.
When sound goes from one medium to another, unchanged quantity is
Q40.
Speed of sound is maximum in
Q41.
The ratio of intensities of waves y₁ = 0.06 sin 2π(0.04t + 0.1x) and y₂ = 0.03 sin 2π(0.08t + 0.2x) is
Q42.
A man hears thunder 6s after lightning (T = 27°C). Distance is (v₀ = 332 m/s)
📅IOM 2001
Q43.
A man hears echo on 3rd clap (2 claps/s). Distance if v = 320 m/s is
📅IOM 1998
Q44.
Two uniform wires with diameter ratio 1:2 under same tension have frequency ratio
📅MOE 2066
Q45.
Phase difference between y₁ = a sinωt and y₂ = a cosωt is
📅MOE 2008
Q46.
The equation y = 10 sinπ(0.01x - 2t) has frequency
📅MOE 2063
Q47.
Frequency of 15 MHz radio waves has wavelength
📅MOE 2056
Q48.
Ratio of intensities of y₁ = 20sin8π and y₂ = 40sin100π is
📅MOE 2063
Q49.
For sound wave (f = 500 Hz, v = 350 m/s), distance between particles with 60° phase difference is
Q50.
In y = Y₀ sin2π(ft - x/λ), if v_max = 4v_wave then
Q51.
For y = 6cos(1800t - 60x), ratio of maximum particle velocity to wave velocity is
Q52.
A string (L=0.6m, μ=0.2 kg/m) vibrates in 3 segments (A=0.5cm) at T=80N. Particle velocity amplitude is
Q53.
Speed of sound in moist H₂ vs dry H₂ is
Q54.
String stretched by 20% has wave speed v. If stretched by 16%, new speed is
📅MOE
Q55.
Time for sound to travel 1m in steel rod (Y=2×10¹¹ N/m², ρ=8000 kg/m³) is
Q56.
Depth of sea if echo returns in 2s (B=2.3×10⁹ N/m², ρ=1.1 g/cc) is
Q57.
Percentage change in speed of sound when T increases from 300K to 301K is
Q58.
Amplitude at 40cm compared to 10cm is
Q59.
Ratio of amplitudes at 9m and 25m from point source is
Q60.
If pressure amplitude increases by 1%, intensity increases by
Q61.
Intensity of sound in air (ρ=1.3 kg/m³, v=330 m/s, P=1.01×10⁵ Pa) is
Q62.
For y = 5/[5 + (x+30)²], maximum displacement is
Q63.
For y = 2/[2 + (x+20)²], wave velocity is
Q64.
For y = 5/[5 + (4x+50)²]
Q65.
Displacement changes from y = 1 + x² at t=0 to y = 1 + (x-1)² at t=2s. Velocity is
Q66.
Ratio of sound speed in H₂ (γ=7/5) to He (γ=5/3) at same T is
Q67.
Jet plane sound heard at 30° when overhead has velocity (sound speed = v)
Q68.
Ripple tank pulses at 0.1s intervals create 30mm spacing. New spacing at 0.5s intervals is
Q69.
1000 Hz wave travels 600m in 2s. Number of wavelengths in this distance is
Q70.
Cloud at 60° elevation produces thunder after 8s (v=300 m/s). Height is
Q71.
If note B has 1/8th frequency of A with equal energy, amplitude of B is
Q72.
For gas with sound speeds v₁,v₂ at T₁,T₂ and rms speeds v₁',v₂'
Q73.
Two wires with density ratio 1:3 have frequency ratio
📅IOM 2017
Q74.
Velocity of sound in steel (Y=2×10¹¹ N/m², ρ=78×10³ kg/m³) is
📅IOM 2017