Question 11 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 21 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 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
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 41 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 51 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 61 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 71 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 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
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 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:
$\text{y}=2\sqrt{\text{x}-\text{vt}}$
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 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:
$\text{y}=2\cos(3\text{x})\sin(10\text{t})$
AnswerThe given equation represents a stationary wave because the harmonic terms kx and ωt appear separately in the equation.
View full question & answer→Question 121 Mark
Two sitar strings A and B playing the note ‘Dha’ are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B is slightly increased and the beat frequency is found to decrease to 3 Hz. What is the original frequency of B if the frequency of A is 427 Hz ?
AnswerIncrease in the tension of a string increases its frequency. If the original frequency of $B \left(v_B\right)$ were greater than that of $A \left(v_A\right)$, further increase in $v_B$ should have resulted in an increase in the beat frequency. But the beat frequency is found to decrease. This shows that $v_B<v_A$. Since $v_A-v_B=5 Hz$, and $v_A=427 Hz$, we get $v_B=422 Hz$.
View full question & answer→Question 131 Mark
A steel wire $0.72 m$ long has a mass of $5.0 \times 10^{-3} kg$. If the wire is under a tension of $60 N$, what is the speed of transverse waves on the wire?
AnswerMass per unit length of the wire,
$
\begin{aligned}
\mu & =\frac{5.0 \times 10^{-3} kg }{0.72 m } \\
& =6.9 \times 10^{-3} kg m ^{-1}
\end{aligned}
$
Tension, $T=60 N$
The speed of wave on the wire is given by
$
v=\sqrt{\frac{T}{\mu}}=\sqrt{\frac{60 N }{6.9 \times 10^{-3} kg m ^{-1}}}=93 m s ^{-1}
$
View full question & answer→Question 141 Mark
Given below are some examples of wave motion. State in each case if the wave motion is transverse, longitudinal or a combination of both:
(a) Motion of a kink in a longitudinal spring produced by displacing one end of the spring sideways.
(b) Waves produced in a cylinder containing a liquid by moving its piston back and forth.
(c) Waves produced by a motorboat sailing in water.
(d) Ultrasonic waves in air produced by a vibrating quartz crystal.
Answer(a) Transverse and longitudinal
(b) Longitudinal
(c) Transverse and longitudinal
(d) Longitudinal
View full question & answer→Question 151 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 161 Mark
State the factors on which the speed of a wave travelling along a stretched ideal string depends.
AnswerSpeed depends on Tension and Mass per unit length.
View full question & answer→Question 171 Mark
Name the apparatus used to demonstrate the phenomenon of the reflection of waves.
Question 181 Mark
In which type of wave alternate crests and troughs are formed?
Question 191 Mark
Can sound waves be propagated in all the three states of matter?
Question 201 Mark
Fundamental frequency of oscillation of a close pipe is 400Hz. What will be the fundamental frequency of oscillation of an open pipe of same length?
Question 211 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 221 Mark
How many beats are formed when two sources vibrate in unison?
AnswerNo beats are formed, since vb = V1 - V2.
View full question & answer→Question 231 Mark
How can we distinguish between a violin and a sitar note?
AnswerThe quality of sound and overtones produced will be different. So, we can identify.
View full question & answer→Question 241 Mark
What is the nature of waves produced in a tuning fork?
AnswerIn tuning forks, standing waves are produced with antinode at the free ends.
View full question & answer→Question 251 Mark
Name the waves which do not require any material medium for their propagation.
AnswerNon-mechanical or electromagnetic waves.
View full question & answer→Question 261 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 271 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 281 Mark
Which type of waves exhibit polarisation?
Question 291 Mark
Why is it difficult some times to recognise your friends voice on phone?
Question 301 Mark
Why bells are made of metal and not wood?
AnswerThis is because wood has high damping.
View full question & answer→Question 311 Mark
An observer is stationed at x = 10cm. When a train moves in the y-axis with a velocity 10m/s, what is the apparent frequency?
AnswerThere is no Doppler shift in perpendicular direction, so no apparent frequency.
View full question & answer→Question 321 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 331 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 341 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 351 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 361 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 371 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 381 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 391 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 401 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 411 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 421 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 431 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 441 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 451 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 $v_\text{s}<v.$ When $v_\text{s}>v,$ shock waves are produced.
View full question & answer→Question 461 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 471 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 481 Mark
In an open organ pipe, third harmonic is 450Hz. What is the frequency of fifth harmonic?
Answer$\because \text{v}_3=3\text{v}_1$
$\text{v}_3=450\text{Hz}$
$\therefore 450=3\text{v}_1$
$\Rightarrow\text{v}_1=150\text{Hz}$
Fifth harmonic,
$\text{v}_5=5\text{v}_1$
$=5\times150$
$\text{v}_5=750\text{Hz}$
View full question & answer→Question 491 Mark
Two sound sources produce 12 beats in 4 seconds. By how much do that frequencies differ?
AnswerBeat frequency $=\frac{12}{4}=3\text{beats/ sec}.$
View full question & answer→Question 501 Mark
_______ waves do not transfer any energy and momentum in the material medium.
AnswerStanding waves do not transfer any energy and momentum in the material medium.
View full question & answer→