71

Chapter 14

Waves

ASSIGNMENT

Single Choice Type Questions

1. Two waves of frequencies 6 Hz and 10 Hz are superposed. The beat frequency produced is
(1) 6 Hz (2) 10 Hz
(3) 16 Hz (4) 4 Hz
2. Two waves of wavelengths 99 cm and 100 cm produce 4 beats per second. Velocity of sound in the medium is
(1) 100 m/s (2) 99 m/s
(3) 196 m/s (4) 396 m/s
3. A set of 10 tuning forks is arranged in series of increasing frequency. If each fork gives 3 beats with the
preceding one and the last fork has twice the frequency of the first, then frequency of the first tuning fork is
(1) 30 Hz (2) 27 Hz
(3) 33 Hz (4) 15 Hz
4. Which of the following characteristics of sound help us in identifying two persons talking in a room without
seeing them?
(1) Loudness (2) Pitch
(3) Quality (4) Intensity
5. A tuning fork of unknown frequency produces 4 beats per second when sounded with another tuning fork of
frequency 254 Hz. It gives the same number of beat/s when loaded with wax. The unknown frequency is
(1) 258 (2) 254
(3) 250 (4) Can’t be determined
 πx 
6. The equation of standing wave in a stretched string
= is given by y 5 sin   cos(40πt ) where x and y are in
 3 
cm and t in second. The separation between two consecutive nodes is (in cm)
(1) 1.5 (2) 3
(3) 6 (4) 4
7. The string of a violin has a fundamental frequency of 440 Hz. If the violin string is shortened by one fifth, its
fundamental frequency will be changed to
(1) 440 Hz (2) 880 Hz
(3) 550 Hz (4) 2200 Hz

Corporate Office : Aakash Tower, 8, Pusa Road, New Delhi-110005. Phone : (011)-47623456
 72 JEE SCORE for Main-2024 Waves

8. A wave moves with a certain speed in a stretched string. The percentage change in tension required to
increase the velocity by 1%, is approximately

(1) 1% increase

(2) 1% decrease

(3) 2% increase

(4) 2% decrease

9. The amplitude of a wave represented by the equation y = 3 sin(5x – 0.5 t) + 4 cos (5x – 0.5 t), is

(1) 7 (2) 4

(3) 3 (4) 5

10. The equation of a wave on a string of linear mass density 0.04 kg m–1 is given by

  t x 
=y 0.02(m )sin 2π  –  .
  0.04(s ) 0.50(m )  

The tension in the string is

(1) 6.25 N

(2) 4.0 N

(3) 12.5 N

(4) 0.5 N

11. A travelling wave represented by y = A sin(ωt – kx) is superimposed on another wave represented by
y = A sin(ωt + kx). The resultant is

nλ
(1) A standing wave having nodes at x = ; n = 0, 1, 2 ….
2

 1 λ
x  n +  ; n = 0, 1, 2 ….
(2) A standing wave having nodes at =
 2 2

(3) A wave travelling along +x direction

(4) A wave travelling along –x direction

12. Statement-1 : Two longitudinal waves given by equations : y1(x, t) = 2a sin (ωt – kx) and y2(x, t) = a sin (2ωt –

2kx) will have equal intensity.

Statement-2 : Intensity of waves of given frequency in same medium is proportional to square of amplitude
only.

(1) Statement-1 is true, statement-2 is true; statement-2 is not correct explanation of statement-1

(2) Statement-1 is false, statement-2 is true

(3) Statement-1 is true, statement-2 is false

(4) Statement-1 is true, statement-2 is true; statement-2 is the correct explanation of statement-1

Corporate Office : Aakash Tower, 8, Pusa Road, New Delhi-110005. Phone : (011)-47623456
 Waves JEE SCORE for Main-2024 73

13. The figure represents a snapshot at time t = 0 of transverse sine wave travelling in a string in the positive x-
direction. If the angular frequency of the wave is 100 rad/s then the velocity of point marked A at this instant is

(1) −250 jˆ mm/s (2) 250 jˆ mm/s

(3) −250 3 jˆ mm/s (4) 250 3 jˆ mm/s

14. A sine wave is travelling in a string in the positive x-direction, with speed v. The shape of a part of the string at
time t = t0 is as shown. The equation of the wave may be given as

π 
(1) y a0 cos  ( x − vt )
=
b 

 π 
(2) y a0 cos  ( x − vt + vt0 )
=
 2b 

 π 
(3) y a0 cos  ( x − vt − vt0 )
=
 2b 

 π 
(4) y a0 sin  ( x − vt − vt0 )
=
 2b 

Assertion-Reason Type Questions

15. STATEMENT-1 : The change in pitch of sound depends on speed of source and detector relative to each other
and not on the distance between them.

and

STATEMENT-2 : The pitch of sound depends on intensity of sound which is independent of distance between
source and detector.

(1) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

(2) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

(3) Statement-1 is True, Statement-2 is False

(4) Statement-1 is False, Statement-2 is True

Corporate Office : Aakash Tower, 8, Pusa Road, New Delhi-110005. Phone : (011)-47623456
 74 JEE SCORE for Main-2024 Waves

Numerical Value Type Questions

16. A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP.
Assuming the speed of sound in air at STP in 300 m/s, the frequency difference between the fundamental and
second harmonic of this pipe is _______ Hz.

17. A wire of density 9 × 10–3 kg cm–3 is stretched between two clamps 1 m apart. The resulting strain in the wire
is 4.9 × 10–4. The lowest frequency of the transverse vibrations in the wire is (Young’s modulus of wire
Y= 9 × 1010 Nm–2), (to the nearest integer), __________.

18. The percentage increase in the speed of transverse waves produced in a stretched string if the tension is
increased by 4% will be ________%.

19. A wire having a linear mass density 9.0 ×10–4 kg/m is stretched between two rigid supports with a tension of
900 N. The wire resonates at a frequeucy of 500 Hz. The next higher frequency at which the same wire
resonates is 550 Hz. The length of the wire is ___ m.

20. Consider the situation shown in the figure. The wire of mass m gram oscillates in its fundamental mode and
sets the air column in the tube in its third harmonic. If the tension in the wire is 260.1 N and the speed of sound
in air is 340 ms–1, the value of 10m is __________ [Neglect end effect].

21. Two coherent narrow slits emitting sound of wavelength λ in the same phase are placed parallel to each
other at a small separation of λ . The sound is detected by moving a detector on the screen at a distance
2
D = 100 3 m (D >> λ) from the slit S1 (see figure). d is the distance (in m) from O such that path difference
at P equals half the path difference at O. The value of d is __________.
10

22. The equation of a standing wave produced on a string fixed at both ends is
 π  
y (0.2 cm) sin  cm−1  x  sin[(400π s−1 ) t ] , where one end of the string is at x = 0 and the other end at x =
 25  
L. The smallest possible value of L (in cm) is __________.

  

Corporate Office : Aakash Tower, 8, Pusa Road, New Delhi-110005. Phone : (011)-47623456