ALLEN JEE-Physics 1

ENTHUSIAST COURSE
ADDITIONAL QUESTIONS
ON
SOUND WAVE
1. Three sound waves of equal amplitudes have frequencies (n–1), n, (n+1). They superpose to give
beats. The number of beats produced per second will be :-
(A) 2 (B) 1 (C) 4 (D) 3
2. Four tuning forks of frequencies 200, 201, 205 and 206 Hz are sounded together. The beat fre-
quency will be-
(A) 6 (B) 12 (C) 15 (D) None of these
3. Two sound waves of frequencies 100 Hz and 102 Hz and having same amplitude 'A' are interfering.
A detector which can detect waves of amplitude greater than or equal to A is kept at rest. In a time
interval of 12 seconds, find the total duration (in sec) in which detector is active.
4. Two electric trains run at the same speed of v = 90 km/hr along a straight track one after the other
with an interval of l = 2.0 km between them. At the instant when they are located symmetrically
relative to point A at a distance of b = 1.0 km from the track (figure) both trains give a brief sound
signal of the same frequency of n = 50 Hz. What will the number of beats heard per second at
point A when the vibrations produced by the signals arrive at it ? The speed of sound is
v = 350 m/s. Round off to nearest integer.

5. For displacement(s)-x graph shown for a sound wave, select appropriate excess pressure(p)-x graph.
s

p p

(A) x (B) x

p p

(C) x (D) x

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2 Additional Questions on Sound Wave ALLEN
6. Mark the INCORRECT statement about longitudinal pressure wave.
(A) The density variation and the longitudinal velocity of the particles have their maxima and
minima at the position of equilibrium of the particles.
(B) At the position of maximum displacement the density is at the ambient (environment) value.
(C) Greatest compression occurs at the same time and place where the velocity of the particles is
maximum and in direction of wave propagation.
(D) Greatest rarefaction occurs at the same time and place where the velocity of the particles is
maximum and in direction of wave propagation.
Paragraph For Question No. 7 to 10 (4 questions)
A plane pressure pulse triangular in shape approaches a rigid wall along normal at a speed of 400
m/s. At time t = 0, situation is shown in the figure. The peak pressure is 100 P. By the wall pulse
gets reflected and pressure near the wall gets doubled. Height of the wall is 2m and width is also
2m. A detector on the wall records a minimum excess pressure of 16 pascal.

7. When for the first time detector will record the pressure pulse
(A) 22 × 10–2 s (B) 21 × 10–2 s (C) 31.5 × 10–2 s (D) None of these
8. For how much time the detector will record the pulse
(A) 37.5 × 10–2 s (B) 34.5 × 10–2 s (C) 31.5 × 10–2 s (D) None of these
9. What is the maximum force applied by the pulse on the wall
(A) 400 N (B) 800 N (C) 200 N (D) None of these
10. Total impulse imparted by the pulse on the wall will be
(A) 300 Ns (B) 150 Ns (C) 750 Ns (D) None of these
11. If the adjacent figure shows the displacement-time curve of common medium particle for two
sound waves A and B propagating in the same medium, the ratio of their intensities IA / IB = X.
Find the value of X.

Displacement (mm)
2× 10
-2
A
-2
10
B time(s)
1 2 3 4
-2 100 100 100 100
-10

12. A small source of sound operates at 1kHz,24pW emitting sound uniformly in all directions.The
speed of sound is 360m/s in air and density of air is 1.2kg/m3.
(A) The intensity of sound at a distance 10m from the source is 0.06W/m2
(B) The intensity of sound at a distance 10m from the source is 0.24W/m2
(C) The pressure amplitude at distence 10m is 7.2 Pa
(D) The pressure amplitude at distence 10m is 28.8 Pa

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 ALLEN JEE-Physics 3
13. In the Kundts tube experiment [shown in figure (i)], the rod is clamped at the end instead of clamping
it at the center as shown in [figure (ii)]. It is known that speed of sound in air is
330 m/s, powder piles up at successive distance of 0.6 m and length of rod used is 1m, speed of
sound in rod is
(i) Standard Kundt's tube (ii) Modified Kundt's tube

clamp clamp
rod movable piston rod movable piston

powder heap powder heap

(A) 550 m/s (B) 1100 m/s (C) 1200 m/s (D) 600 m/s
14. In a pipe open at two ends a diatomic gas is oscillating in 1st harmonic. The length of the tube is p
m and the maximum pressure variation is 1.4 Pa. The maximum displacement of gas particles
p
which are a distance of m from one end is x × 10–6m. The value of x is (Take 1 atm = 105 Pa)
3
15. Sound waves of frequency 320Hz are sent into the top of a vertical tube containing water at a
level that can be adjusted. Standing waves are produced at two successive water levels 44cm and
74cm from open end. The distance of nearest displacement antinode from open end (in cm) is.

44cm

74cm
water

(A) 1 (B) 2 (C) 3 (D) 4

16. In an organ pipe (which may be closed or open) of 99 cm length, standing wave is set up whose

equation is given by longitudinal displacement x = 0.3 mm cos éêæç 2 p ö÷ ( z + 0.01m ) ùú cos (400 t),
ëè 0.8 ø û
where z is measured from the top of tube in metres and t is in seconds. Take end correction
= 1 cm. Choose CORRECT statement(s) :-
(A) The upper end and lower end of tube are open and closed respectively. z=0
Upper
(B) The upper end and lower end of tube are closed and open respectively. end
(C) The air column is vibrating in third harmonic. z
(D) The air column is vibrating in second overtone. lower
17. Mark the CORRECT statement (s) :- end
(A) When two waves of different frequency f1 and f2 are superimposed at a point, the variation of
intensity takes place with frequency f1 – f2
(B) When an observer is moving, relative speed of the sound waves with respect to the observer
is changed, while due to motion of source, the sound wavelength of the wave changes.
(C) When a high pressure compression pulse reaches water surface in a resonance column, it
reflects as a low pressure rarefraction pulse due to a phase change of p
(D) When a tuning fork is struck by a hammer a transverse wave sets in the prong while a
longitudinal wave sets in the stem (handle) of tuning fork

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4 Additional Questions on Sound Wave ALLEN
18. The 5 graphs shown in column-II are plots of displacement from mean position at a given instant. The
arrows represent the direction of velocity of particles at that moment. Match with description in column-
I.
Column I Column II

(A) Standing wave (P)

x
All velocities are along negative x.

(B) Wave travelling along x > 0 (positive x) (Q)

x
All velocities are along negative y.

(C) Wave travelling along x < 0 (negative x) (R)

x
Half of the velocities are along negative y and
other half are along positive y.

(D) Longitudinal wave (S)

x
Half of the velocities are along negative x and
other half are along positive x.

(T)
x
Half of the velocities are along negative x and
other half are along positive x.

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 ALLEN JEE-Physics 5
19. In a resonance column apparatus, first resonance is obtained when the water filling beaker
(of cylindrical shape) is just empty as shown. The water filling beaker is lowered down and it is
seen that second resonance is obtained when beaker is filled upto brim. The wavelength of sound
a
is given by m. Find the value of a.
10

2cm

4cm
10cm

20. As shown above there is two circles having radius R and 2R respectively. Sound source is moving
in inner circle in anticlockwise direction. Observer is moving on outer circle in clockwise direction
with angular velocity w1 and w2 respectively. If frequency of source is f then, frequency observed
by observer is (Given: w1 = 10 rad/sec, w2 = 10 rad/s, R = 10 m and velocity of sound is 330 m/s)

2R
observer
R 60°

source

23 47 43
(A) f (B) f (C) f (D) f
43 23 23
21. A sonic oscillator of high frequency f0 is moving along a long straight road with constant speed v
(v is comparable to the speed of sound). A stationary observer is at a distance 'b' from the road .
Then the graph of frequency as heard by the observer verses x-coordinate of source as observed
by the observer is best represented by

f f f
f0
f0
(A) f0 (B) f0 (C) x (D) x

x x

22. A man while sitting on an oscillating swing whistles at a frequency 1000 Hz. The swing is
p
oscillating with an amplitude ± radian about the mean position in a vertical plane. Man is
6
sitting over the swing which is at a distance of 2m from the point of suspension of the swing.
Another man standing just infront of the mean position of the swing hears the whistle. The
maximum frequency heard by the man standing in front of the swing is : (Speed of sound in
air = 332 m/s)

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6 Additional Questions on Sound Wave ALLEN
23. Two trains move in the same direction on two close tracks. The train A sounds a horn of single
frequency of 1 kHz. At a certain instant of time, when both trains move at the same speed of 36
km/hr, the two straight tracks deviate at an angle of 60° with each other. Velocity of sound in air
is 300 m/s. Which of the following statement(s) is/are true ?

1 uA=36 km/h uA
60°

2 uB =36 km/h
uB

(A) The apparent frequency heard by a passenger on the second train B just after he passes the
bend will be 1.05 kHz.
(B)The apparent frequency heard by a passenger on the first train A, just after the second train B
passes the bend will be 1 kHz.
(C) The apparent frequency heard by a passenger on the second train B just after he passes the
bend will be 983 Hz.
(D) If the first train A, that produces the sound, were to pass the bend while the other train B goes on
the straight track then the apparent frequency heard by a passenger on the latter train B will be less
than 1kHz.
24. Consider :
Case-1 : A moving source moving with velocity vs and a stationary receiver.
Case-2 : A moving receiver moving with velocity vR and a stationary source.
In either case fR represents frequency heard by receiver and fS represents frequency emitted by

fR
source. Figure shows graph of on y axis and vs or vR on x axis. Mark the CORRECT option (s)
fS

fR
Graph-1 fS

1 Graph-2

vR or vs
–v O +v

(A) Graph–1 corresponds to moving receiver and Graph-2 corresponds to moving source.
(B) Graph–2 corresponds to moving receiver and Graph-1 corresponds to moving source.
(C) Graphs to left of origin represents approaching listener and to right represents receding listener
(D) Graphs to right of origin represents approaching source and to left represents receding source

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 ALLEN JEE-Physics 7
Paragraph for Question No. 25 to 28 (4 questions)
A source emitting a sound wave at a certain frequency moves with constant speed along an x-axis figure
(a). The source moves directly towards a stationary detector A and directly away from another stationary
detector B. The superimposed three plots of figure (b) indicate the pressure function P(x) of the sound
wave as measured by detector A, by detector B, and by someone (c) in the rest frame of the source.

25. Which of the following plot corresponds to the measurement done by detector A?
(A) 1 (B) 2
(C) 3 (D) These plots are not possible
26. The plot corresponding to the measurement done by detector B is
(A) 1 (B) 2
(C) 3 (D) These plots are not possible
27. The plot corresponding to the measurement done by the detector C is
(A) 1 (B) 2
(C) 3 (D) These plots are not possible
28. Now the source stops and begins to move along y-axis with same speed, the plot which corresponds
to the measurement of B now is
(A) 1 (B) 2 (C) 3 (D) none of these
29. Two tuning forks A and B each of natural frequency 85 Hz move with velocity 10 m/s relative to
stationary observer ‘O’. Fork A moves away from the observer while the fork B moves towards him
as shown in the figure. A wind with a speed 10 m/s is blowing in the direction of motion of fork A.
Find the beat frequency measured by the observer (in Hz). [Take speed of sound in air as 340 m/s]

A B
O

30. In a kundt's tube experiment metallic rod of length 1m is clamped from the distance of 25 cm from
one end. If distance between heap of powder 50 cm and speed of sound in air is 330 m/s select correct
statement(s) :-
(A) Frequency in which tube is oscillating is 1320 Hz 25cm
(B) Frequency in which tube is oscillating is 330 Hz 50cm
1m
(C) Velocity of wave in metallic rod is 330 m/s
(D) Velocity of wave in metallic rod is 1320 m/s

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8 Additional Questions on Sound Wave ALLEN
Paragraph for Question No. 31 to 34 (4 questions)
Imagine that you are in Indian army and you have been given charge of commanding parade on
26th January. The soldiers have done extensive training on march past with a band which strikes
120 times/min. The soldier should strike left foot or right foot at each drum beat so that parade
marches at 120 steps/min.
On the day of parade, there are 2 parts. In 1st part, the band marches ahead of the soldiers with same
speed as that of soldiers. In this march, you notice that the soldiers in the first row strike left foot
but the soldiers in last row strike right foot at the same time. Unfortunately, the general also notices
this.
In the 2nd part, you hope & pray that everything goes well. In this part, the band is stationary but
the soldiers advance towards the band at same constant speed. Here again, you notice that the
soldiers in the parade are doing 121 steps/min. As before, the general notices this.
A court martial is due for you. You frantically try to look for an explanation. One of your friends
reminds you of your old physics teacher at Allen. You turn to him for solace. He suggests two
things for defence.
(a) Sound takes time to reach from one place to another.
(b) doppler’s effect
Assume that it was chilly winter & speed of sound = 320 m/sec.
31. Select the correct explanation for mistakes in each part.
(A) part I ® a, part II ® b (B) part I ® a, part II ® a
(C) part I ® b, part II ® a (D) part I ® b, part II ® b
32. What can be the length of the column of soldiers marching past.
(A) 320 m (B) 160 m (C) 80 m (D) 40 m
33. What is the speed of the soldiers.
(A) 1.0 m/s (B) 2.0 m/s (C) 1.5 m/s (D) 2.5 m/s
34. What will be the marching speed of the soldiers when they turn around & march away from the band
in part 2 ?
(A) 120 steps/min. (B) 119 steps/min. (C) 121 steps/min. (D) 110 steps/min.
Paragraph for Question no. 35 to 37
The Doppler flow meter is a particularly interesting medical application of the Doppler effect.
This device measures the speed of blood flow, using transmitting and receiving elements that are
placed directly on the skin, as in Figure. The transmitter emits a continuous sound whose fre-
quency is typically about 5 MHz. When the sound is reflected from the red blood cells, its fre-
quency is changed in a kind of Doppler effect because the cells are moving with the same veloc-
ity as the blood. The receiving element detects the reflected sound, and an electronic counter
measures its frequency, which is Doppler-shifted relative to the transmitter frequency. From the
change in frequency the speed of the blood flow can be determined. Typically, the change in
frequency is around 600 Hz for flow speeds of about 0.1 m/s.

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 ALLEN JEE-Physics 9
35. Assume that the red blood cell is directly moving away from the source and the receiver. What is the
(approx) speed of the sound wave in the blood?
(A) 1700 m/s (B) 330 m/s (C) 5000 m/s (D) 3000 m/s
36. An abnormal segment of the artery is narrowed down by an arteriosclerotic plaque to one-fourth
the normal cross-sectional area. What will be the change in frequency due to reflection from the
red blood cell in that region?
(A) 150 Hz (B) 300 Hz (C) 600 Hz (D) 2400 Hz
37. At what extra rate does the heart have to work due to this narrowing down of the artery? Assume
the density to be 1.5 gm/cc and the area of the normal artery to be 0.1 cm2.
(A) 1.125 × 10–4 W (B) 2.5 × 10–4 W (C) 6.25 × 10–5 W (D) 5.625 × 105 W
38. A sonic source is moving in a circle of radius 10 m, emitting sound of frequency 1000 Hz. It is
moving with a constant speed = 110 m/s, and speed of sound in air = 330 m/s. A stationary
detector is located at a point 20 m from the centre of the circular path of the source, in the same
plane. Suppose the detector which can detect only waves whose frequency is less than 1000 Hz
remains idle during a time interval Dt, in one revolution of the source. Find Dt / T, where T = time
period of revolution of source.
39. A supersonic jet plane moves parallel to the ground at speed v = 0.75 mach (1 mach = speed of
sound). The frequency of its engine sound is n0 = 2 kHz and the height of the jat plane is h = 1.5
km. At some instant an observer on the ground hears a sound of frequency n = 2 n0, Find the
instant prior to the instant of hearing when the sound wave received by the observer was emitted
by the jet plane. Velocity of sound wave in the condition of observer = 340 m/s.
40. Three coherent sonic sources emitting sound of single wavelength l are placed on the x-axis at

æ -l 11 ö æ l 11 ö æ 5l ö
points çç 6 , 0 ÷÷ , ( 0, 0 ) , çç 6 , 0 ÷÷ . The intensity reaching a point ç 0, ÷ from each source
è ø è ø è 6 ø

has the same value I0. Then, the resultant intensity at this point due to the interference of the three
waves will be :-
(A) 6I0 (B) 7I0 (C) 9I0 (D) 5I0
Paragraph for question nos. 41 to 44
A detector at x = 0 receives waves from three sources each of amplitude A and frequencies f + 2, f and
f – 2.
41. The equations of waves are: y1 = Asin[2p(f + 2)t], y2 = Asin2pft and y3 = Asin[2p(f – 2)t]
The time at which intensity is minimum:
(A) t = 0, 1/4, 1/2, 3/4, ¼ sec (B) t = 1/6, 1/3, 2/3, 5/6, ¼ sec
(C) t = 0, 1/2, 3/2, 5/2, ¼ sec (D) t = 1/2, 1/4, 1/6, 1/8, ¼ sec
42. The time at which intensity is maximum
(A) t = 0, 1/4, 1/2, 3/4, ¼ sec (B) t = 1/6, 1/3, 2/3, 5/6, ¼ sec
(C) t = 0, 1/2, 3/2, 5/2, ¼ sec (D) t = 1/2, 1/4, 1/6, 1/8, ¼ sec
43. If I0aA , then the value of maximum intensity is
2

(A) 2I0 (B) 3I0 (C) 4I0 (D) 9I0

44. The detector can measure intensity greater than 4A . The idle time for the detector is 1 s is
2

(A) 1/2 s (B) 1/3 s (C) 2/3 s (D) 1/4 s

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10 Additional Questions on Sound Wave ALLEN
45. The three identical loud speakers in figure play a 170 Hz frequency tone in a room where speed of
sound is 340 m/s. At point exactly infront of source S2 the amplitude of the wave from each speaker
is a. What is ratio of resultant intensity at P and intensity due to single speaker.

S1
3m
S2
P

3m

S3
4m

46. AB is a cylinder of length 1.0 m filled with a thin flexible adibatic membrane C (see figure) at the
middle and two other thin flexible adiabatic membranes A and B at the ends. The portions AC and
BC contain hydrogen and oxygen gasses respectively at same pressure. Standing waves are setup in
two columns such that membrane A acts as antinode and B as node (speed of sound in oxygen is 330
m/s) The frequency of these vibrations for which the membrane C is a node is :
C
A B

(A) 330 Hz (B) 550 Hz (C) 1485 Hz (D) 660 Hz

47. A loudspeaker L is placed in the hall with two doors D1 and D2 open to the playground, as shown
below. The distance between D1 and D2 is 74.25 m . The loudspeaker L is equidistant from D1 and
D2. Monotonic sound waves are emitted from the loudspeaker, and it is found that at both points P &
Q, sound intensities are minimum. Distance of point P from D1 is 6m. The line joining D1, P and Q is
perpendicular to the line joining D1 and D2. No other minimum intensity locations can be found
between PQ and beyond Q along the PQ line. The wavelength in metre of the sound wave generated
by the loudspeaker is.........

D2
L Hall
D1
P Q

Paragraph for Question no. 48 and 49

Three sound waves represented by
p1 = p 0 sin 400pt , p 2 = p 0 sin 404pt and p 3 = p 0 sin 408pt
superimpose at origin. p is the pressure fluctuation. p0 is the maximum pressure fluctuation.
48. The number of beats heard per second will be
(A) 2 (B) 4 (C) 8 (D) 10

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 ALLEN JEE-Physics 11
49. Intensity variation for superposition of three waves as a function of time is given as

I I

(A) (B)
t(s) t(s)
O 0.25 0.5 0.75 1 O 0.25 0.5 0.75 1

(C) (D) none of these

t(s)
O 0.25 0.5 0.75 1

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50. Two sound waves of slightly different frequencies have amplitude ratio . What is the difference of
9
sound levels in decibels of maximum and minimum intensities heard at a point :-
(A) 100 (B) 10 (C) 16 (D) 20
51. In the experiment to determine the speed of sound using a resonance column,
(A) prongs of the tuning fork are kept in a vertical plane
(B) prongs of the tuning fork are kept in a horizontal plane
(C) in one of the two resonances observed, the length of the resonating air column is close to the
wavelength of sound in air
(D) in one of the two resonances observed, the length of the resonating air column is close to half
of the wavelength of sound in air
Paragraph for Question Nos. 52 to 54
Two trains A and B are moving with speeds 20 m/s and 30 m/s respectively in the same direction on
the same straight track, with B ahead of A. The engines are at the front ends. The engine of train A
blows a long whistle. Assume that the sound of the whistle is composed to components varying in
frequency from f1 = 800 Hz to f2 = 1120 Hz, as shown in the figure. The spread in the frequency
(highest frequency – lowest frequency) is thus 320 Hz. The speed of sound in still air is 340 m/s

52. The speed of sound of the whistle is

(A) 340 m/s for passengers in A and 310 m/s for passengers in B
(B) 360 m/s for passengers in A and 310 m/s for passengers in B
(C) 310 m/s for passengers in A and 360 m/s for passengers in B
(D) 340 m/s for passengers in both the trains

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12 Additional Questions on Sound Wave ALLEN
53. The distribution of the sound intensity of the whistle as observed by the passengers in train A is best
represented by

(A) (B)

(C) (D)

54. The spread of frequency as observed by the passengers in train B is

(A) 310 Hz (B) 330 Hz (C) 350 Hz (D) 290 Hz
55. While measuring the speed of sound by performing a resonance column experiment, a student
gets the first resonance condition at column length of 18 cm during winter. Repeation the same
experiment during sumer, student measures the column length to be x cm for the second resonance.
Then
(A) 18 > x (B) x > 54 (C) 54 > x > 36 (D) 36 > x > 18
56. A vibrating string of certain length l under a tension T reasonates with a mode corresponding to
the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one
end. The string also generates 4 beats per second when excited along with a tuning fork of frequency
n. Now when the tension of the string is slightly increased the number of beats reduces to 2 per
second. Assuming the velocity of sound in air to be 340 m/s, the frequency n of the tuning fork in
Hz is.
(A) 344 (B) 336 (C) 117.3 (D) 109.3

Additional Questions Answer key

1. Ans. (A) 2. Ans. (A) 3. Ans. 8 4. Ans. 5 5. Ans. (A) 6. Ans. (D)
7. Ans. (B) 8. Ans. (B) 9. Ans. (B) 10. Ans. (B) 11. Ans. 001 12. Ans. (A,C)
13. Ans. (B) 14. Ans. 5 15. Ans. (A) 16. Ans. (A, D) 17. Ans. (A,B, D)
18. Ans. (A) PQ (B) RS (C) T (D) PST 19. Ans. 8 20. Ans. (C)
21. Ans. (D) 22. Ans. 1007 23. Ans. (B,C,D) 24. Ans. (A, C) 25. Ans. (A)
26. Ans. (B) 27. Ans. (C) 28. Ans. (D) 29. Ans. 5 30. Ans. (B,C)
31. Ans. (A) 32. Ans. (B) 33. Ans. (D) 34. Ans. (B) 35. Ans. (A)
36. Ans. (D) 37. Ans. (A) 38. Ans. (3p–2)/6p 39. Ans. 5.9 sec
40. Ans. (B) 41. Ans. (B) 42. Ans. (A) 43. Ans. (D) 44. Ans. (C)
45. Ans. 1 46. Ans. (D) 47. Ans. 3 48. Ans. (B) 49. Ans. (D)
50. Ans. (D) 51. Ans. (A) 52. Ans. (B) 53. Ans. (A) 54. Ans. (A)
55. Ans. (B) 56. Ans. (A)