❖ 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
❖ 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.
Phase difference between the particles at P and Q is:
📅CEE MBBS 2025
Q2.
If pressure amplitude of sound wave is doubled, intensity becomes
📅CEE MBBS 2025
Q3.
The range of 10⁵ Hz frequency is:
📅CEE Nursing 2024
Q4.
In electromagnetic wave, phase relation of electric and magnetic waves is:
📅CEE Nursing 2024
Q5.
Speed of sound is greater in solids than in liquid because:
📅CEE Nursing 2024
Q6.
If the temperature increases by 1°C, then the change in velocity of sound is (v at NTP = 332 m/s):
📅CEE MBBS 2024B
Q7.
A man heard thunder 6 seconds after he saw a lightning flash. The temperature of air is 27°C. How far was the flash from the man? (Velocity of sound in air at 0°C is 332 m/s)
📅CEE MBBS 2024a
Q8.
Speed of sound is greater in solids than in liquids because:
📅CEE MBBS 2022
Q9.
A change in temperature of the medium changes which property of a sound wave?
📅CEE MBBS 2022
Q10.
Sound travels through medium because
📅CEE MBBS 2021
Q11.
The velocity of sound is more in:
📅CEE BDS 2024
Q12.
Normal hearing range of human is:
📅CEE BDS 2023
Q13.
Two points on a progressive wave differ in phase by \(60^\circ\). If wave speed is \(360\,\mathrm{m/s}\) and frequency \(500\,\mathrm{Hz}\), find their nearest separation.
📅BP 2013•BP 2012
Q14.
Among the following, which material has the highest *typical longitudinal* sound speed? Use representative values: iron 5.1 km/s, granite 6.0 km/s, gold 3.2 km/s, and silver 3.6 km/s.
Q15.
At the same temperature and pressure, equal volumes of \(\mathrm{H_2}\) and \(\mathrm{O_2}\) are mixed. Approximating the adiabatic indices as equal, find the ratio of sound speed in the mixture to that in pure \(\mathrm{O_2}\). Take molar masses \(2\) and \(32\).
📅BP 2012
Q16.
How are phase difference \(\Delta\phi\) (in radians) and path difference \(\Delta x\) related for a wave of wavelength \(\lambda\)?
📅BP 2011
Q17.
Which phenomenon is uniquely characteristic of transverse mechanical waves?
📅BP 2010
Q18.
Which frequency range is ordinarily audible to a young healthy human?
📅BP 2010
Q19.
Why may sound travelling near the ground be heard more clearly over a long distance at night?
📅IOM 2013
Q20.
What kinds of mechanical elastic waves can propagate inside a rock?
📅IOM 2009
Q21.
The speed of sound in air is \(330\,\mathrm{m/s}\) near \(0^\circ\mathrm C\). Taking a rise of about \(0.6\,\mathrm{m/s}\) per °C, how far does sound travel in \(2\,\mathrm s\) at \(30^\circ\mathrm C\)?
📅MOE 2013
Q22.
For a resonance tube of radius \(R\), what is the approximate end correction at its open end?
📅MOE 2013
Q23.
A sound pulse travels between a rigid reflecting wall and a second reflecting surface at the listener, separated by \(s\). Each complete round trip yields another echo. If sound speed is \(V\), when is the second round-trip echo heard?
📅MOE 2012
Q24.
Speed of sound in water is \(1400\,\mathrm{m/s}\) and water density is \(1000\,\mathrm{kg/m^3}\). Find its bulk modulus.
📅MOE 2012
Q25.
Why is Laplace’s adiabatic correction needed in Newton’s formula for the speed of sound in air?
📅MOE 2010
Q26.
In an ideal transverse mechanical wave, what is the angle between particle oscillation velocity and the direction of wave propagation?
📅MOE 2010
Q27.
Each of two identical blocks absorbs 10% of the sound intensity entering it. What percentage of the initial intensity emerges from the second block?
📅MOE 2009
Q28.
A medium has adiabatic elastic modulus \(E_a\) and isothermal elastic modulus \(E_i\). For sound propagation at fixed density, the sound speed is proportional to:
📅MOE 2009
Q29.
When the temperature of air changes, which property of a sound wave from a fixed-frequency source changes?
📅KU 2014
Q30.
Which listed wave is mechanical and requires a material medium?
📅KU 2012
Q31.
A radio transmitter emits electromagnetic waves of wavelength \(30\,\mathrm m\). Find their frequency in vacuum.
📅IOM 2012
Q32.
At \(0^\circ\mathrm C\), speed of sound in air is \(332\,\mathrm{m/s}\). What is the approximate increase in speed for a \(10^\circ\mathrm C\) temperature rise?
Q33.
Helium has molar mass \(4\,\mathrm{g/mol}\). Find sound speed in helium at \(0^\circ\mathrm C\) using \(\gamma=5/3\) and \(R=8.314\,\mathrm{J/(mol\,K)}\).
Q34.
Two motions are \(x=a\sin(\omega t+\pi/6)\) and \(x^{\prime}=a\cos\omega t\). Find their phase difference.
Q35.
Two waves are \(y=a\sin(\omega t-kx)\) and \(y^{\prime}=b\cos(\omega t-kx)\). What is their phase difference?
Q36.
Two waves of equal amplitude are \(y_1=a\sin(\omega t+\pi/6)\) and \(y_2=a\cos\omega t\). Find resultant amplitude.
Q37.
The progressive wave equation is \(y=4\sin[\pi(t/5-x/3)+\pi/6]\), with \(x\) in metres and \(t\) in seconds. Which statement is correct?
Q38.
If the pressure-amplitude of a sound wave triples in the same medium, by what factor does its intensity change?
Q39.
At a fixed temperature and composition of an ideal gas, sound speed is essentially independent of a change in:
📅IOM 2001
Q40.
Which frequency is within the usual audible range of human hearing?
Q41.
At what Celsius temperature will sound speed in air double compared with its value at \(27^\circ\mathrm C\)?
Q42.
Air is initially at fixed temperature with sound speed \(300\,\mathrm{m/s}\). If pressure is quadrupled *isothermally*, what is the sound speed?
Q43.
At the same temperature, find \(v_{H_2}:v_{O_2}\), assuming both gases have the same adiabatic index. Molar masses are \(2\) and \(32\,\mathrm{g/mol}\).
Q44.
A gas mixture contains hydrogen and oxygen in a \(4:1\) volume ratio. Approximate both gases as having the same adiabatic index. If sound speed in hydrogen is \(1270\,\mathrm{m/s}\) at the same conditions, find the speed in the mixture.
Q45.
What is the minimum distance from a reflecting wall needed to hear a distinct echo, taking sound speed \(330\,\mathrm{m/s}\) and auditory persistence time \(0.1\,\mathrm s\)?
Q46.
A homogeneous string of length \(L\) and mass \(M\) hangs vertically under its own weight. Find the transverse-wave speed at a point a distance \(x\) above its freely hanging lower end.
Q47.
A right-moving transverse wave \(y=A\sin(\omega t-kx)\) reaches an ideal fixed boundary. Which expression represents its left-moving reflected wave?
Q48.
What is the smallest path difference between two points on a progressive wave corresponding to a \(60^\circ\) phase difference?
Q49.
How is a transverse displacement pulse reflected from a fixed end of a taut string?
Q50.
A person stands between two cliffs and hears the first two echoes of a clap after \(1\,\mathrm s\) and \(2\,\mathrm s\), one from each cliff. If sound speed is \(340\,\mathrm{m/s}\), find the distance between the cliffs.
Q51.
When sound passes from one material medium to another, which quantity remains unchanged?
Q52.
For hypothetical ideal gases having the same molar mass and temperature, which molecular type has the highest speed of sound when vibrations are inactive?
Q53.
Two plane waves propagate in the same medium: \(y_1=0.06\sin[2\pi(0.04t+0.1x)]\) and \(y_2=0.03\sin[2\pi(0.08t+0.2x)]\). Find the ratio of their average intensities.
Q54.
A person hears thunder \(6\,\mathrm s\) after seeing lightning in air at \(27^\circ\mathrm C\). Estimate the distance, using \(v_0=332\,\mathrm{m/s}\) at 0°C and \(0.6\,\mathrm{m/(s\,K)}\) per degree.
📅IOM 2001
Q55.
A person claps uniformly at \(2\) claps per second. An echo of the first clap is heard simultaneously with the third clap. If sound speed is \(320\,\mathrm{m/s}\), how far away is the reflecting wall?
📅IOM 1998
Q56.
Two strings of the same material and length, with diameter ratio 1:2, are stretched under the same tension. Find the ratio of fundamental frequencies.
📅MOE 2066
Q57.
Find the phase difference between \(y_1=a\sin\omega t\) and \(y_2=a\cos\omega t\).
📅MOE 2008
Q58.
A travelling wave is described by \(y=10\sin[\pi(0.01x-2t)]\), with \(t\) in seconds. What is its frequency?
📅MOE 2063
Q59.
Find the wavelength of radio waves with frequency \(15\,\mathrm{MHz}\) in vacuum.
📅MOE 2056
Q60.
Two plane mechanical waves in the same medium have equations \(y_1=20\sin(8\pi t)\) and \(y_2=40\sin(100\pi t)\). Find the ratio of average intensities (same units for amplitude).
📅MOE 2063
Q61.
For sound frequency \(500\,\mathrm{Hz}\) and speed \(350\,\mathrm{m/s}\), find the separation corresponding to a \(60^\circ\) phase difference.
Q62.
For \(y=Y_0\sin[2\pi(ft-x/\lambda)]\), the maximum particle speed is four times the wave speed. Express \(\lambda\) in terms of \(Y_0\).
Q63.
A wave has displacement \(y=6\sin(1800t-60x)\), where \(y\) is measured in \(\mu\mathrm m\), \(x\) in metres and \(t\) in seconds. Find the ratio of maximum particle speed to wave-propagation speed.
Q64.
A string of length \(0.6\,\mathrm m\), linear mass density \(0.2\,\mathrm{kg/m}\), and tension \(80\,\mathrm N\) vibrates in three loops with amplitude \(0.5\,\mathrm{cm}\). Find maximum particle speed.
Q65.
At the same temperature and total pressure, how does the speed of sound in moist hydrogen compare with that in dry hydrogen?
Q66.
The same elastic string supports transverse waves of speed \(v\) when its fractional extension is \(20\%\). Approximately what is the speed when extension is \(16\%\), assuming Hooke’s law and negligible change in linear density?
📅MOE
Q67.
Find the time for a longitudinal sound pulse to travel \(1\,\mathrm m\) along a steel rod with \(Y=2\times10^{11}\,\mathrm{Pa}\) and \(\rho=8000\,\mathrm{kg/m^3}\).
Q68.
A sonar echo from the seabed returns after \(2\,\mathrm s\). Find sea depth if water has bulk modulus \(2.3\times10^9\,\mathrm{Pa}\) and density \(1.1\,\mathrm{g/cm^3}\).
Q69.
What is the approximate percentage increase in sound speed when the absolute temperature of a gas rises from \(300\,\mathrm K\) to \(301\,\mathrm K\)?
Q70.
At \(10\,\mathrm{cm}\) from an isotropic point sound source, the displacement amplitude is \(A\). What is it at \(40\,\mathrm{cm}\) in the far field, neglecting absorption?
Q71.
Find the ratio of displacement amplitudes at \(9\,\mathrm m\) and \(25\,\mathrm m\) from an isotropic point sound source, assuming spherical spreading.
Q72.
If pressure amplitude of a sound wave increases by 1%, what is the approximate percentage increase in intensity?
Q73.
A plane sound wave in air has *peak acoustic pressure amplitude* \(p_0=1.01\times10^5\,\mathrm{Pa}\), density \(\rho=1.3\,\mathrm{kg/m^3}\), and sound speed \(v=330\,\mathrm{m/s}\). Under the linear-wave formula, find its mean intensity.
Q74.
A pulse profile is \(y=5/[5+(x+30)^2]\), with \(y\) in centimetres. What is its maximum displacement?
Q75.
A travelling pulse is described by \(y(x,t)=2/[2+(x+20t)^2]\), where \(x\) is in centimetres and \(t\) in seconds. Find the magnitude of the pulse speed.
Q76.
A pulse is described by \(y(x,t)=5/[5+(4x+50t)^2]\), where \(x\) is in centimetres and \(t\) in seconds. Which statement is correct?
Q77.
At \(t=0\), a pulse has profile \(y=1+x^2\), and at \(t=2\,\mathrm s\) its profile is \(y=1+(x-1)^2\), with \(x\) in metres. Find its propagation speed.
Q78.
For ideal gases \(\mathrm{H_2}\) (\(\gamma=7/5\), \(M=2\)) and He (\(\gamma=5/3\), \(M=4\)) at the same absolute temperature, find \(v_{H_2}/v_{He}\).
Q79.
A supersonic aircraft produces a Mach cone of half-angle \(30^\circ\). If the speed of sound is \(v\), what is the aircraft speed?
Q80.
A ripple tank produces pulses \(0.1\,\mathrm s\) apart, separated by \(30\,\mathrm{mm}\). What will be their spacing if the interval is changed to \(0.5\,\mathrm s\) without altering wave speed?
Q81.
A wave of frequency \(1000\,\mathrm{Hz}\) travels \(600\,\mathrm m\) in \(2\,\mathrm s\). How many wavelengths fit in the 600-metre distance?
Q82.
A thundercloud is at elevation angle \(60^\circ\) above the horizontal. Thunder is heard \(8\,\mathrm s\) after lightning, and sound speed is \(300\,\mathrm{m/s}\). Neglect light travel time; find cloud height above the observer.
Q83.
Two oscillations have equal energy, but B has one-eighth the frequency of A. Assuming identical effective mass, find amplitude ratio \(A_B/A_A\).
Q84.
For the *same ideal gas*, let sound speeds be \(v_1,v_2\) at temperatures \(T_1,T_2\), and molecular RMS speeds be \(u_1,u_2\). Which relation is correct?
Q85.
Two otherwise identical wires under equal tension have material-density ratio 1:3. Find their fundamental-frequency ratio.
📅IOM 2017
Q86.
Find the longitudinal sound speed in steel with \(Y=2\times10^{11}\,\mathrm{Pa}\) and \(\rho=7.8\times10^3\,\mathrm{kg/m^3}\).
