Part - II of the
Quick Silver Test Series . This time we bring for you an array of chosen problems on Waves.
Q1.A wave is traveling along a string. At an instant, shape of the string is as shown in figure. At this instant, point A is moving upwards. Which of the following statements is/are correct?
(a) The wave is traveling to the right.
(b) Displacement amplitude of the wave in equal to displacement of B at this instant.
(c) At this instant velocity of C is also directed upwards.
(d) Phase difference between A and C may be equal to  . |
 |
Q2.A plane sound wave to traveling in a medium. In reference to a frame A, its equation is y = a cos (
t – kx). In reference to a frame B, moving with a constant velocity
v in the direction of propagation of the wave, equation of the wave will be:
| (a) |
y = a cos [( + kv)t – kx] |
(b) |
y = – a cos [( + kv)t – kx] |
| (c) |
y = a cos [(– kv)t – kx] |
(d) |
y = a cos [( + kv)t + kx] |
Q3.A sonic source, located in a uniform medium, emits waves of frequency n. If intensity, energy density (energy per unit volume of the medium) and maximum speed of oscillations of medium particles are respectively I, E and u
0 at a point, which of the following graphs is incorrect?
Q4.The displacement‑time graphs for two sound waves A and B are shown in the figure. Then the ratio of their intensities I
A/I
B is equal to:
| (a) |
1 : 4 |
(b) |
1 : 16 |
(c) |
1 : 2 |
(d) |
1 : 1. |
Q5.It is found that an increase in pressure of 100 kP
a causes a certain volume of water to decrease by 5 x 10
–3 percent of its original volume. Then the speed of sound in the water is about:
| (a) |
330 m/s |
(b) |
1400 m/s |
(c) |
2400 m/s |
(d) |
660 m/s |
Q6.A traveling wave in a gas along the positive x‑direction has an amplitude of 2 cm, velocity 45 m/s and frequency 75 Hz. The maximum particle acceleration is:
| (a) |
0.44 x 102 cm/s2 |
(b) |
4.4 x 105 cm/s2 |
(c) |
4.4 x 103 cm/s2 |
(d) |
44 x 105 cm/s2 |
Q7.Taking the composition of air to be 75% of N
2 and 25% of oxygen by weight, what is the velocity of sound through air at 16°C ?
| (a) |
3 10 m/s |
(b) |
341 m/s |
(c) |
360 m/s |
(d) |
450 m/s |
Q8.If the velocity of sound in air is 320 m/s, the maximum and minimum length of a pipe closed at one end, that would produce a just audible sound, are:
| (a) |
2.6 m and 3.6 x 10–3 m |
(b) |
4 m and 4.2 x 10–3 m |
| (c) |
3 m and 3 x 10–3 m |
(d) |
4 m and 4 x 10–3 m |
Q9.Which of the following graphs, between the frequency n and square root of density (
) of a wire, keeping its length, radius and tension constant, is correct ?
Q10.A uniform rope of mass M = 0. 1 kg and length L = 10 m hangs from the ceiling.
(a) Speed of the transverse wave in the rope increases linearly from bottom to the top.
(b) Speed of the transverse wave in the rope decreases linearly from bottom the top.
(c) Speed of the transverse wave in the rope remains constant along the length of the rope.
(d) Time taken by the transverse wave to travel the full length of the rope is 2 sec.
Q11.Which of the following statements is correct for waves ?
(a) Nodes and anti‑nodes are formed in case of transverse stationary waves only.
(b) Nodes and anti‑nodes are formed in case of longitudinal stationary wave only.
(c) Nodes and anti‑nodes are formed in case of all the stationary waves.
(d) None of these.
Q12.A steel wire is stretched between two walls and excited in its fundamental tone. Which of the following statements is correct ?
(a) On increasing the temperature, frequency of fundamental tone increases.
(b) On decreasing the temperature, frequency of fundamental tone decreases.
(c) Frequency of fundamental tone does not vary with temperature.
(d) None of these.
Q13.A string is fixed at both ends and transverse oscillations with amplitude a0 are excited. Which of the following statements is/are correct ?
(a) Energy of oscillations in the string is directly proportional to tension in the string.
(b) Energy of oscillations in the string inversely proportional to tension in the string.
(c) Energy of oscillations1w the string is directly proportional to length of the string.
(d) Energy of oscillations in the string is independent of length of the string.
Q14.Mark correct statement(s)
(a) To observe interference, two sources of slightly different frequencies are required.
(b) To observe interference, two sources of same frequency must be placed some distance apart from each other.
(c) To observe interference, two sources must have same frequency and same amplitude.
(d) None of these.
Q15.Velocity of sound in air is 320 ms–1. A pipe closed at one end has a length of 1 m. If end correction is neglected then the pipe cannot resonate at:
| (a) |
80 Hz |
(b) |
240 Hz |
(c) |
320 Hz |
(d) |
400 Hz |
Q16.How long will it take for the sound waves to travel a distance
l from point A to point B, if the temperature between these points changes linearly from T
1 to T
2 and the velocity of sound propagation in air is
where
is a constant ?
Q17.All the strings shown in the figure are identical. The pulleys are massless and frictionless. The ratio of speeds of transverse waves in the strings AB and CD will be :
| (a) |
1 |
(b) |
 |
(c) |
 |
(d) |
2 |
Q18.The equation y = a sin
2 (kx –
t) represents a traveling wave whose
Q19.Two wires of radii r and 2r respectively are welded together end to end. The combination is used as a sonometer wire and is kept under a tension T. The welded point is midway between the bridges. What would be the ratio of the number of loops formed in the wires such that the joint is a node, when stationary vibrations are set up in the wires ?
| (a) |
1 : 1 |
(b) |
1 : 2 |
(c) |
2 : 1 |
(d) |
1 : 4 |
Q20.The frequency of a sonometer wire is f. But when the weights producing the tensions are completely immersed in water, the frequency becomes f/2 and on immersing the weights in a certain liquid, the frequency becomes f/3. The specific gravity of the liquid is:
| (a) |
1.320 |
(b) |
1.032 |
(c) |
1.413 |
(d) |
1.185 |
Q21.A string of length
l is stretched by
l/10 and the velocity of transverse waves along it is V. When it is stretched by
l/20 (Assuming Hook's law is applicable), the velocity of wave will become:
Q22.A wave represented by y = a cos (kx ‑
vt) is superimposed with another wave to produce stationary wave, such that x = 0 is a node. The equation of the other wave is
| (a) |
y = a sin (kx + vt) |
(b) |
y = – a cos (kx – vt) |
(c) |
y = – a cos (kx + vt) |
(d) |
y = – a sin (kx – vt) |
Q23.Consider ten identical sources of sound all giving the same frequency but having phase angles which are random. If the average intensity of each source is
Io, the average of resultant intensily
I due to all these ten sources will be :
| (a) |
I = 100 Io |
(b) |
I = 10 Io |
(c) |
I = Io |
(d) |
 |
Q24.In a large room, a person receives direct sound waves from a source 120 metres away from him. He also receives waves from the same source which reach, being reflected from the 25 metre high ceiling at a point half‑way between them. The two waves interfere constructively for wavelength (in m) of :
| (a) |
20, 20/3, 20/5 etc. |
(b) |
10, 5, 2.5 etc. |
(c) |
10, 20, 30 etc. |
(d) |
15, 25, 35 etc. |
Q25.Two tuning forks of frequency 250 Hz and 256 Hz produce beats. If a maximum is observed just now, after how much time the minimum is observed at the same place ?
| (a) |
1/18 sec |
(b) |
1/24 sec |
(c) |
1/6 sec |
(d) |
1/12 sec |
Q26.The extension in a string, obeying Hooke's law is x. The speed of sound in the stretched string is
v. If the extension in the string is increased to 1.5 x, the speed of sound will be:
| (a) |
1.22 v |
(b) |
0.61 v |
(c) |
1.50 v |
(d) |
0.75 v |
Q27. A hollow metallic tube of length L and closed at one end produces resonance with a tuning fork of frequency f. The entire tube is heated carefully so that length changes by
l. If the change in velocity V of the sound is
v. The resonance will now be produced by tuning fork whose frequency is:
| (a) |
(V + v)/4 (L + l) |
(b) |
(V – v)/(L – l) |
(c) |
(V + v)/4 (L – l) |
(d) |
(V – v)/4 (L + l) |
Q28.Sonic source is moving in a circular orbit of radius 4m with angular velocity of 8 radian/sec anticlockwise. A detector executes S.H.M. of amplitude 6m at a large distance from the source between points E and F. The frequency of oscillation of the detector is  When the source is at point C then the detector is at point E. The source emits sound of frequency 330 Hz. The maximum frequency detected by the detector will be, when the source is at: |
 |
Q29.A jet fighter flies in a straight line over an airfield with a speed of 200 m/s, level with the ground at a height of 400 m. It is emitting a continuous note of frequency 1.1 kHz. Then the change in frequency as detected by a detector on ground, over 3.0 s interval as the jet flies over (given the speed of sound in air = 340 m/s), is
| (a) |
1.7 kHz |
(b) |
468 Hz |
(c) |
887 Hz |
(d) |
776 Hz |
Q30.The difference between the apparent frequency of a stationary source of sound as received by an observer during its approach and recession is 2 % of the natural frequency of the source. If the velocity of sound in air is 300 m/s, the velocity of the source is :
| (a) |
6 m/s |
(b) |
3 m/s |
(c) |
1.5 m/s |
(d) |
12 m/s |
