Question 11 Mark
Explain why (or how):
Solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases,
AnswerThis is because solids have both, the elasticity of volume and elasticity of shape, whereas gases have only the volume elasticity.
View full question & answer→Question 21 Mark
Explain why (or how):
A violin note and sitar note may have the same frequency, yet we can distinguish between the two notes,
AnswerThe overtones produced by a sitar and a violin, and the strengths of these overtones, are different. Hence, one can distinguish between the notes produced by a sitar and a violin even if they have the same frequency of vibration.
View full question & answer→Question 31 Mark
For the travelling harmonic wave
$\text{y}(\text{x, t})=2.0\cos2\pi(10\text{t}-0.0080\text{x}+0.35)$
where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of
0.5m,
AnswerEquation for a travelling harmonic wave is given as:
$\text{y}(\text{x, t})=2.0\cos2\pi(10\text{t}-0.0080\text{x}+0.35)$
$=2.0\cos(20\pi\text{t}-0.016\pi\text{x}+0.70\pi)$
Where,
Propagation constant, $\text{k}=0.0160\pi$
Amplitude, a = 2cm
Angular frequency, $\omega=20\pi\text{ rad/s}$
Phase difference is given by the relation:
$\phi=\text{kx}=\frac{2\pi}{\lambda}$
For x = 0.5m = 50cm
$\phi=0.016\pi\times50=0.8\pi\text{ rad}$
View full question & answer→Question 41 Mark
For the travelling harmonic wave
$\text{y}(\text{x, t})=2.0\cos2\pi(10\text{t}-0.0080\text{x}+0.35)$
where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of
4m.
AnswerEquation for a travelling harmonic wave is given as:
$\text{y}(\text{x, t})=2.0\cos2\pi(10\text{t}-0.0080\text{x}+0.35)$
$=2.0\cos(20\pi\text{t}-0.016\pi\text{x}+0.70\pi)$
Where,
Propagation constant, $\text{k}=0.0160\pi$
Amplitude, a = 2cm
Angular frequency, $\omega=20\pi\text{ rad/s}$
Phase difference is given by the relation:
$\phi=\text{kx}=\frac{2\pi}{\lambda}$
For x = 4 m = 400cm
$\phi=0.016\pi\times400=6.4\pi\text{ rad}$
View full question & answer→Question 51 Mark
Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a travelling wave, (ii) a stationary wave or (iii) none at all:
$\text{y}=\cos\text{x}\sin\text{t}+\cos2\text{x}\sin2\text{t}$
AnswerThe given equation represents a stationary wave because the harmonic terms kx and $\omega\text{t}$ appear separately in the equation. This equation actually represents the superposition of two stationary waves.
View full question & answer→Question 61 Mark
For the travelling harmonic wave
$\text{y}(\text{x, t})=2.0\cos2\pi(10\text{t}-0.0080\text{x}+0.35)$
where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of
$\frac{3\lambda}{4},$
AnswerEquation for a travelling harmonic wave is given as:
$\text{y}(\text{x, t})=2.0\cos2\pi(10\text{t}-0.0080\text{x}+0.35)$
$=2.0\cos(20\pi\text{t}-0.016\pi\text{x}+0.70\pi)$
Where,
Propagation constant, $\text{k}=0.0160\pi$
Amplitude, a = 2cm
Angular frequency, $\omega=20\pi\text{ rad/s}$
Phase difference is given by the relation:
$\phi=\text{kx}=\frac{2\pi}{\lambda}$
For $\text{x}=\frac{3\lambda}{4}$
$\phi=\frac{2\pi}{\lambda}\times\frac{3\lambda}{4}=1.5\pi\text{ rad}$
View full question & answer→Question 71 Mark
A transverse harmonic wave on a string is described by
$\text{y}(\text{x, t})=3.0\sin\big(36\text{t}+0.018\text{x}+\frac{\pi}{4}\big)$
where x and y are in cm and t in s. The positive direction of x is from left to right.
What is the initial phase at the origin?
Answer$\frac{\pi}{4}$
Explanation:
Given,
$\text{y}(\text{x, t})=3\sin\big(36\text{t}+0.018\text{x}+\frac{\pi}{4}\big)$
Initial phase at the origi $=\frac{\pi}{4}$
View full question & answer→Question 81 Mark
For the travelling harmonic wave
$\text{y}(\text{x, t})=2.0\cos2\pi(10\text{t}-0.0080\text{x}+0.35)$
where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of
$\frac{\lambda}{2},$
AnswerEquation for a travelling harmonic wave is given as:
$\text{y}(\text{x, t})=2.0\cos2\pi(10\text{t}-0.0080\text{x}+0.35)$
$=2.0\cos(20\pi\text{t}-0.016\pi\text{x}+0.70\pi)$
Where,
Propagation constant, $\text{k}=0.0160\pi$
Amplitude, a = 2cm
Angular frequency, $\omega=20\pi\text{ rad/s}$
Phase difference is given by the relation:
$\phi=\text{kx}=\frac{2\pi}{\lambda}$
For $\text{x}=\frac{\lambda}{2}$
$\phi=\frac{2\pi}{\lambda}\times\frac{\lambda}{2}=\pi\text{ rad}$
View full question & answer→Question 91 Mark
Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a travelling wave, (ii) a stationary wave or (iii) none at all:
$\text{y}=3\sin(5\text{x}-0.5\text{t})+4\cos(5\text{x}-0.5\text{t})$
AnswerThe given equation represents a travelling wave as the harmonic terms kx and ωt are in the combination of $\text{kx}-\omega\text{t}.$
View full question & answer→Question 101 Mark
Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a travelling wave, (ii) a stationary wave or (iii) none at all:
$\text{y}=2\cos(3\text{x})\sin(10\text{t})$
AnswerThe given equation represents a stationary wave because the harmonic terms kx and ωt appear separately in the equation.
View full question & answer→Question 111 Mark
Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a travelling wave, (ii) a stationary wave or (iii) none at all:
$\text{y}=2\sqrt{\text{x}-\text{vt}}$
AnswerThe given equation does not contain any harmonic term. Therefore, it does not represent either a travelling wave or a stationary wave.
View full question & answer→Question 121 Mark
For the harmonic travelling wave $\text{y}=2\cos2\pi(10\text{t}-0.0080\text{x}+3.5)$ where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of:
$\frac{\lambda}{2}$
Answer$\text{y}=2\cos2\pi(10\text{t}-0.0080\text{x+3.5})$
$\text{y}=2\cos(20\pi\text{t}-0.0016\pi\text{x}+7.0\pi)$
Wave is propagated in $+\text{x}$ direction because $\omega\text{t}$ and kx are in with opposite sign standard equation $\text{y}=\text{a}\cos(\omega\text{t}-\text{kx}+\phi)$
a = 2, $\omega=20\pi,\ \text{k}=0.016\pi$ and $\phi=7\pi$
Path difference $\text{p}=\frac{\lambda}{2}$
$\Delta\phi=\frac{2\pi}{\lambda}\text{p}=\frac{2\pi}{\lambda}\times\frac{\lambda}{2}\pi\ \text{radian}$
View full question & answer→Question 131 Mark
Explain why (or how):
Solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases,
AnswerThis is because solids have both, the elasticity of volume and elasticity of shape, whereas gases have only the volume elasticity.
View full question & answer→Question 141 Mark
What is the condition to be satisfied by a mathematical relation between time and displacement to describe a periodic motion?
Answer$\text{y}=\text{a}\sin(\text{wt}-\phi_0).$ Similar displacement should happen at regular time intervals 18.
View full question & answer→Question 151 Mark
In the given progressive wave $\text{y}=5\sin(100\pi\text{t+0.4x})$ where y and x are in m, t is in s. What is the:Frequency
AnswerStandard form of progressive wave travelling in $+\text{x}$ direction (kx and $\omega\text{}t$ have opposite sign is given)
Eqn. is $\text{y}=\text{a}\sin(\omega\text{t}-\text{kx}+\phi)$
$\text{y}=5\sin(100\pi\text{t}-0.4\pi\text{t}+0)$
Frequency $\text{v},\omega=2\pi\text{v}\Rightarrow\text{v}=\frac{\omega}{2\pi}\because\omega=100\pi$
$\therefore\text{v}=\frac{100\pi}{2\pi}=50\text{Hz}$
View full question & answer→Question 161 Mark
Can sound waves be propagated in all the three states of matter?
Question 171 Mark
What is the distance between a compression and its nearest rarefaction in a longitudinal wave?
AnswerDistance between a compression and adjoining rarefaction is $\frac{\lambda}{2}.$
View full question & answer→Question 181 Mark
Is it possible to have longitudinal waves on a string a transverse wave in a steel rod?
AnswerNo, because string is not stretchable. It can neither be compressed nor rarefied. Yes, transverse waves are possible in steel rod, because steel has elasticity of shape.
View full question & answer→Question 191 Mark
What do you mean by reverberation time?
AnswerThe time during which the intensity of sound decreases to $10^{-6}$ times its original intensity.
View full question & answer→Question 201 Mark
Why does the speed of sound differ from a solid and a liquid medium of same length?
AnswerModulus of elasticity differs from the solid to liquid. Since side ways variation of elasticity is absent in liquids, only bulk modulus is used and not Young's modulus.
View full question & answer→Question 211 Mark
Why do stationary waves not transport energy?
AnswerSince nodes and antinodes formed remain stationary, the energy remains confined to one region. It cannot overcome the pressure maxima at nodes. So, energy is not transmitted by standing waves.
View full question & answer→Question 221 Mark
In a dispersive medium, how will you express the velocity of wave motion?
AnswerSpeed of a wave is expressed as $\frac{\text{d}\omega}{\text{dk}}$ for dispersive medium.
View full question & answer→Question 231 Mark
Why should the difference between the frequencies be less than ten to produce beats?
AnswerHuman ear cannot identify any change in intensity in less than $\Big(\frac{1}{10}\Big)^{\text{th}}$ of a second. So, difference should be less than 10.
View full question & answer→Question 241 Mark
In the given progressive wave $\text{y}=5\sin(100\pi\text{t+0.4x})$ where y and x are in m, t is in s. What is the:
Wave velocity
AnswerStandard form of progressive wave travelling in $+\text{x}$ direction kx and $\omega\text{}t$ have opposite sign is given) Eqn. is $\text{y}=\text{a}\sin(\omega\text{t}-\text{kx}+\phi)$ $\text{y}=5\sin(100\pi\text{t}-0.4\pi\text{t}+0)$Wave velocity $\text{v}=\text{v}\lambda=50\times5=250\text{m/ s}$
View full question & answer→Question 251 Mark
What is the relation between velocity of the wave (v) frequency of the wave (v) and wavelength of the wave $(\lambda)$?
Answer$\text{v}=\text{v}\lambda$
View full question & answer→Question 261 Mark
What propagates faster-a radio signal or sound in the air?
Question 271 Mark
What change is observed when a wave gets reflected from a hard, rigid support?
AnswerA phase change of $\pi$ radians.
View full question & answer→Question 281 Mark
Given below are some functions of x and t to represent the displacement of an elastic wave.
$\text{y}=4\sin(5\text{x}-\text{t/ 2})+3\cos(5\text{x}-\text{t/ 2})$
AnswerA stationary wave of the for $\text{y}=5\cos(4\text{x})\sin20\text{t}$ is a stationary wave so (b) (i).
View full question & answer→Question 291 Mark
Write two characteristics of a medium which determine the speed of sound waves in the medium.
Answer
- Elasticity of medium.
- Inertia of medium.
View full question & answer→Question 301 Mark
What is the source of the non-mechanical waves?
AnswerThey are produced due to the changes of the electric and magnetic fields associated with the moving changes.
View full question & answer→Question 311 Mark
What is the nature of ultrasonic waves and what is their frequency?
AnswerUltrasonic waves are longitudinal waves in nature and have frequency greater than 20kHz.
View full question & answer→Question 321 Mark
Why is sound heard in water more intense in comparison to sound heard in air?
AnswerThis is because intensity of sound increases with increase in density of the medium.
View full question & answer→Question 331 Mark
An observer places his ear at the end of a long steel pipe. He can hear two sounds, when a workman hammers the other end of the pipe. Why?
AnswerThis is because sound is transmitted both through air and medium.
View full question & answer→Question 341 Mark
Can two astronauts talk on the surface of moon as they do on earth?
AnswerNo, the astronauts cannot talk on the surface of moon as there is no atmosphere (air) on moon. Sound waves cannot travel without a medium.
View full question & answer→Question 351 Mark
For the harmonic travelling wave $\text{y}=2\cos2\pi(10\text{t}-0.0080\text{x}+3.5)$ where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of:0.5m
Answer$\text{y}=2\cos2\pi(10\text{t}-0.0080\text{x+3.5})$
$\text{y}=2\cos(20\pi\text{t}-0.0016\pi\text{x}+7.0\pi)$
Wave is propagated in $+\text{x}$ direction because $\omega\text{t}$ and kx are in with opposite sign standard equation $\text{y}=\text{a}\cos(\omega\text{t}-\text{kx}+\phi)$
a = 2, $\omega=20\pi,\ \text{k}=0.016\pi$ and $\phi=7\pi$
Path differencee p = 0.5m = 50cm
$\Delta\phi=\text{kp}=0.016\pi\times50=0.8\pi$ red.
View full question & answer→Question 361 Mark
Resonance is an example of________.
AnswerResonance is an example of forced vibration.
View full question & answer→Question 371 Mark
How does velocity of sound in air change when temperature rises by 1°C?
AnswerVelocity of sound in air increases by 0.61m/s, when temperature rises by 1°C.
View full question & answer→Question 381 Mark
How is the vibration of the air column in a flute different from that of a string in a sitar?
AnswerThe nodes in a sitar are replaced by the antinodes in a flute.
View full question & answer→Question 391 Mark
Two astronauts on the surface of moon cannot talk to each other. Why?
AnswerThis is because moon has no atmosphere and sound cannot travel in vacuum.
View full question & answer→Question 401 Mark
Does sound travel faster on a wet hot day or a dry cold day? Why?
AnswerSound travels faster on a wet hot day due to high temperature and lesser density of wet air.
View full question & answer→Question 411 Mark
Can mechanical waves travel through vacuum?
AnswerNo, mechanical waves cannot travel through vacuum.
View full question & answer→Question 421 Mark
Explain why (or how):
A violin note and sitar note may have the same frequency, yet we can distinguish between the two notes,
AnswerThe overtones produced by a sitar and a violin, and the strengths of these overtones, are different. Hence, one can distinguish between the notes produced by a sitar and a violin even if they have the same frequency of vibration.
View full question & answer→Question 431 Mark
What is the nature of thermal changes in air, when a sound wave propagates through it?
AnswerWhen a sound wave travels through air, the changes in pressure and volume are adiabatic, i.e., temperature rises in the region of compression and temperature falls in the region of rarefaction.
View full question & answer→Question 441 Mark
Why is it difficult some times to recognise your friends voice on phone?
Question 451 Mark
Why are longitudinal waves called pressure waves?
AnswerThis is because propagation of longitudinal waves through a medium involves changes in pressure and volume of air, when compressions and rarefactions are formed.
View full question & answer→Question 461 Mark
In which gas, hydrogen or oxygen, will sound have greater velocity?
AnswerSince $\nu\propto\sqrt{\frac{1}{\rho}},$ therefore velocity of sound will be greater in hydrogen gas.
View full question & answer→Question 471 Mark
Is air a material medium? Name two characteristics of the material medium necessary for the onward propagation of momentum and energy.
AnswerYes, Inertia and elasticity.
View full question & answer→Question 481 Mark
When a source moves at a speed greater than that of sound, will Doppler formula hold? What will happen?
AnswerNo, as it is valid only when $v_\text{s} When $v_\text{s}>v,$ shock waves are produced.
View full question & answer→Question 491 Mark
What is the phase difference between the waves $\text{y}=\text{a}\cos(\omega\text{t}+\text{kx})$ and $\text{y}=\text{a}\sin (\omega\text{t}+\text{kx})?$
AnswerPhase difference $=\frac{\pi}{2}=90^\circ.$
View full question & answer→Question 501 Mark
Which type of waves exhibit polarisation?