Waves
154 Questions
Start JEE Mains Test
2019
Q101
JEE Mains
MCQ
10 Mar 2026
A progressive wave travelling along the positive x-direction is represented by y(x,t) = Asin(kx – $\omega $t + $\phi $). Its
snapshot at t = 0 is given in the figure.
For this wave, the phase $\phi $ is :
For this wave, the phase $\phi $ is :
A.
${\pi \over 2}$
B.
$\pi $
C.
0
D.
$ - {\pi \over 2}$
2019
Q102
JEE Mains
MCQ
10 Mar 2026
A submarine (A) travelling at 18 km/hr is being chased along the line of its velocity by another submarine
(B) travelling at 27 km/hr. B sends a sonar signal of 500 Hz to detect A and receives a reflected sound of
frequency $\upsilon $. The value of $\upsilon $ is close to: (Speed of sound in water =1500 ms–1)
A.
507 Hz
B.
502 Hz
C.
499 Hz
D.
504 Hz
2019
Q103
JEE Mains
MCQ
10 Mar 2026
A source of sound S is moving with a velocity of 50 m/s towards a stationary observer. The observer
measures the frequency of the source as 1000 Hz. What will be the apparent frequency of the source when it
is moving away from the observer after crossing him? (Take velocity of sound in air is 350 m/s)
A.
750 Hz
B.
857 Hz
C.
807 Hz
D.
1143 Hz
2019
Q104
JEE Mains
MCQ
10 Mar 2026
The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of
frequencies 9 Hz and 11 Hz, is :
A.
B.
C.
D.
2019
Q105
JEE Mains
MCQ
10 Mar 2026
A stationary source emits sound waves of
frequency 500 Hz. Two observers moving
along a line passing through the source detect
sound to be of frequencies 480 Hz and 530 Hz.
Their respective speeds are, in ms–1,
(Given speed of sound = 300 m/s)
A.
12, 18
B.
16, 14
C.
12, 16
D.
8, 18
2019
Q106
JEE Mains
MCQ
10 Mar 2026
A string 2.0 m long and fixed at its ends is
driven by a 240 Hz vibrator. The string vibrates
in its third harmonic mode. The speed of the
wave and its fundamental frequency is :-
A.
180m/s, 80 Hz
B.
180m/s, 120 Hz
C.
320m/s, 120 Hz
D.
320m/s, 80 Hz
2019
Q107
JEE Mains
MCQ
10 Mar 2026
Two cars A and B are moving away from each
other in opposite directions. Both the cars are
moving with a speed of 20 ms–1 with respect
to the ground. If an observer in car A detects
a frequency 2000 Hz of the sound coming from
car B, what is the natural frequency of the sound
source in car B ?
(speed of sound in air = 340 ms–1) :-
(speed of sound in air = 340 ms–1) :-
A.
2300 Hz
B.
2060 Hz
C.
2250 Hz
D.
2150 Hz
$f = {{\left( {v \pm {u_0}} \right)} \over {\left( {v \pm {u_s}} \right)}}.{f_0} = {{\left( {v - 20} \right)} \over {\left( {v + 20} \right)}}.{f_0}$
2019
Q108
JEE Mains
MCQ
10 Mar 2026
The pressure wave, P = 0.01 sin [1000t – 3x] Nm–2,
corresponds to the sound produced by a vibrating blade
on a day when atmospheric temperature is 0°C. On
some other day, when temperature is T, the speed of
sound produced by the same blade and at the same
frequency is found to be 336 ms–1 . Approximate value
of T is
A.
12°C
B.
15°C
C.
4°C
D.
11°C
2019
Q109
JEE Mains
MCQ
10 Mar 2026
A string is clamped at both the ends and it is
vibrating in its 4th harmonic. The equation of the
stationary wave is Y = 0.3 sin(0.157x) cos(200pt).
The length of the string is : (All quantities are
in SI units.)
A.
60 m
B.
20 m
C.
80 m
D.
40 m
2019
Q110
JEE Mains
MCQ
10 Mar 2026
A wire of length 2L, is made by joining two
wires A and B of same length but different radii
r and 2r and made of the same material. It is
vibrating at a frequency such that the joint of
the two wires forms a node. If the number of
antinodes in wire A is p and that in B is q then
the ratio p : q is :
A.
3 : 5
B.
4 : 9
C.
1 : 2
D.
1 : 4
2019
Q111
JEE Mains
MCQ
10 Mar 2026
A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below the reference mark. The velocity of sound in air, obtained in the experiment, is close to :
A.
335 ms–1
B.
328 ms–1
C.
341 ms–1
D.
322 ms–1
2019
Q112
JEE Mains
MCQ
10 Mar 2026
A travelling harmonic wave is represented by the equation y(x,t) = 10–3sin (50t + 2x), where, x and y are in mater and t is in seconds. Which of the following is a correct statement about the wave ?
A.
The wave is propagating along the positive x-axis with speed 100 ms–1
B.
The wave is propagating along the positive x-axis with speed 25 ms–1
C.
The wave is propagating along the negative x-axis with speed 25 ms–1
D.
The wave is propagating along the negative x-axis with speed 100 ms–1
2019
Q113
JEE Mains
MCQ
10 Mar 2026
Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin(450 t – 9x) where distance and time are measured in SI units. The tension in the string is :
A.
10 N
B.
7.5 N
C.
5 N
D.
12.5 N
2019
Q114
JEE Mains
MCQ
10 Mar 2026
A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The string is set into vibration using an external vibrator of frequency 100 Hz. The separation between successive nodes on the string is close to -
A.
16.6 cm
B.
10.0 cm
C.
20.0 cm
D.
33.3 cm
2019
Q115
JEE Mains
MCQ
10 Mar 2026
A train moves towards a stationary observer with speed 34 m/s. The train sounds a whistle and its frequency registered by the observer is ƒ1. If the speed of the train is reduced to 17 m/s, the frequency registered is ƒ2. If speed of sound is 340 m/s, then the ratio ƒ1/ƒ2 is -
A.
19/18
B.
20/19
C.
21/20
D.
18/17
2019
Q116
JEE Mains
MCQ
10 Mar 2026
A musician using an open flute of length 50 cm producess second harmonic sound waves. A person runs towards the musician from another end of hall at a speed of 10 km/h. If the wave speed is 330 m/s, the frequency heard by the running person shall be close to :
A.
666 Hz
B.
753 Hz
C.
500 Hz
D.
333 Hz
2019
Q117
JEE Mains
MCQ
10 Mar 2026
A heavy ball of mass M is suspendeed from the ceiling of a car by a light string of mass m (m < < M). When the car is at rest, the speed of transverse waves in the string is 60 ms$-$1. When the car has acceleration a, the wave-speed increases to 60.5 ms$-$1. The value of a, in terms of gravitational acceleration g, is closest to :
A.
${g \over {30}}$
B.
${g \over 5}$
C.
${g \over 10}$
D.
${g \over 20}$
2018
Q118
JEE Mains
MCQ
10 Mar 2026
The end correction of a resonance column is 1 cm. If the shortest length resonating with the tunning fork is 10 cm, the next resonating length should be :
A.
28 cm
B.
32 cm
C.
36 cm
D.
40 c
2018
Q119
JEE Mains
MCQ
10 Mar 2026
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 s slightly increased and the beat frequency is found to decrease by 3Hz. If the frequency of A is 425 Hz, the original frequency of B is :
A.
430 Hz
B.
420 Hz
C.
428 Hz
D.
422 Hz
2018
Q120
JEE Mains
MCQ
10 Mar 2026
A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The
density of granite is 2.7 $\times$ 103 kg/m3 and its Young’s modulus is 9.27 $\times$ 1010 Pa. What will be the fundamental frequency of the longitudinal vibrations ?
A.
7.5 kHz
B.
5 kHz
C.
2.5 kHz
D.
10 kHz
2018
Q121
JEE Mains
MCQ
10 Mar 2026
5 beats / econd are heard when a tuning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m. The frequency of the fork will be :
A.
195 Hz
B.
150 Hz
C.
300 Hz
D.
251 Hz
2018
Q122
JEE Mains
MCQ
10 Mar 2026
A tuning fork vibrates with frequency $256$ $Hz$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe ? (Speed of sound in air is $340\,m{s^{ - 1}}$)
A.
$220$ $cm$
B.
$190$ $cm$
C.
$180$ $cm$
D.
$200$ $cm$
2017
Q123
JEE Mains
MCQ
10 Mar 2026
A standing wave is formed by the superposition of two waves travelling in
opposite directions. The transverse displacement is given by
y(x, t) = 0.5 sin $\left( {{{5\pi } \over 4}x} \right)\,$ cos(200 $\pi $t).
What is the speed of the travelling wave moving in the positive x direction ?
(x and t are in meter and second, respectively.)
y(x, t) = 0.5 sin $\left( {{{5\pi } \over 4}x} \right)\,$ cos(200 $\pi $t).
What is the speed of the travelling wave moving in the positive x direction ?
(x and t are in meter and second, respectively.)
A.
160 m/s
B.
90 m/s
C.
180 m/s
D.
120 m/s
2017
Q124
JEE Mains
MCQ
10 Mar 2026
In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r1
and r2 . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be
5×10−4 s, the difference in radii, $\left| {} \right.$r1 $-$ r2 $\left| {} \right.$ is best given by :
A.
1 cm
B.
0.05 cm
C.
0.5 cm
D.
0.01 cm
2017
Q125
JEE Mains
MCQ
10 Mar 2026
Two wires W1 and W2 have the same radius r and respective densities $\rho $1 and $\rho $2 such that ρ2 = 4$\rho $1 . They are joined together at the point O, as shown in the figure. The combination is used as a sonometer wire and kept under tension T. The point O is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in W1 to W2
is :
A.
1 : 1
B.
1 : 2
C.
1 : 3
D.
4 : 1
2017
Q126
JEE Mains
MCQ
10 Mar 2026
An observer is moving with half the speed of light towards a stationary microwave source emitting waves
at frequency 10 GHz. What is the frequency of the microwave measured by the observer? (speed of light =
3 ×108 ms–1)
A.
15.3 GHz
B.
10.1 GHz
C.
12.1 GHz
D.
17.3 GHz
2016
Q127
JEE Mains
MCQ
10 Mar 2026
A toy-car, blowing its horn, is moving with a steady speed of 5 m/s, away from a wall. An observer, towards whom the toy car is moving, is able to hear 5 beats per second. If the velocity of sound in air is 340 m/s, the frequency of the horn of the toy car is close to :
A.
680 Hz
B.
510 Hz
C.
340 Hz
D.
170 Hz
2016
Q128
JEE Mains
MCQ
10 Mar 2026
Two engines pass each other moving in opposite directions with uniform speed of 30 m/s. One of them is blowing a whistle of frequency 540 Hz. Calculate the
frequency heard by driver of second engine before they pass each other. Speed of sound is 330 m/sec :
A.
450 Hz
B.
540 Hz
C.
648 Hz
D.
270 Hz
2016
Q129
JEE Mains
MCQ
10 Mar 2026
A uniform string of length $20$ $m$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the supports is :
(take ${\,\,g = 10m{s^{ - 2}}}$ )
(take ${\,\,g = 10m{s^{ - 2}}}$ )
A.
$2\sqrt 2 s$
B.
$2\pi \sqrt 2 s$
C.
$2\pi \sqrt 2 s$
D.
$2$ $s$
2016
Q130
JEE Mains
MCQ
10 Mar 2026
A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :
A.
$2f$
B.
$f$
C.
${f \over 2}$
D.
${3f \over 4}$
2015
Q131
JEE Mains
MCQ
10 Mar 2026
A train is moving on a straight track with speed $20\,m{s^{ - 1}}.$ It is blowing its whistle at the frequency of $1000$ $Hz$. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound $ = 320\,m{s^{ - 1}}$) close to :
A.
$18\% $
B.
$24\% $
C.
$6\% $
D.
$12\% $
2014
Q132
JEE Mains
MCQ
10 Mar 2026
A pipe of length $85$ $cm$ is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below $1250$ $Hz$. The velocity of sound in air is $340$ $m/s$.
A.
$12$
B.
$8$
C.
$6$
D.
$4$
2013
Q133
JEE Mains
MCQ
10 Mar 2026
A sonometer wire of length $1.5$ $m$ is made of steel. The tension in it produces an elastic strain of $1\% $. What is the fundamental frequency of steel if density and elasticity of steel are $7.7 \times {10^3}\,kg/{m^3}$ and $2.2 \times {10^{11}}\,N/{m^2}$ respectively ?
A.
$188.5$ $Hz$
B.
$178.2$ $Hz$
C.
$200.5$ $Hz$
D.
$770$ $Hz$
2012
Q134
JEE Mains
MCQ
10 Mar 2026
A cylindrical tube, open at both ends, has a fundamental frequency, $f,$ in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now :
A.
$f$
B.
$f/2$
C.
$3/4$
D.
$2f$
2011
Q135
JEE Mains
MCQ
10 Mar 2026
The transverse displacement $y(x, t)$ of a wave on a string is given by $y\left( {x,t} \right) = {e^{ - \left( {a{x^2} + b{t^2} + 2\sqrt {ab} \,xt} \right)}}.$ This represents $a:$
A.
wave moving in $-x$ direction with speed $\sqrt {{b \over a}} $
B.
standing wave of frequency $\sqrt b $
C.
standing wave of frequency ${1 \over {\sqrt b }}$
D.
wave moving in $+x$ direction speed $\sqrt {{a \over b}} $
2010
Q136
JEE Mains
MCQ
10 Mar 2026
The equation of a wave on a string of linear mass density $0.04\,\,kg\,{m^{ - 1}}$ is given by
$$y = 0.02\left( m \right)\,\sin \left[ {2\pi \left( {{t \over {0.04\left( s \right)}} - {x \over {0.50\left( m \right)}}} \right)} \right].$$
The tension in the string is
A.
$4.0N$
B.
$12.5$ $N$
C.
$0.5$ $N$
D.
$6.25$ $N$
2009
Q137
JEE Mains
MCQ
10 Mar 2026
Three sound waves of equal amplitudes have frequencies $\left( {v - 1} \right),\,v,\,\left( {v + 1} \right).$ They superpose to give beats. The number of beats produced per second will be :
A.
$3$
B.
$2$
C.
$1$
D.
$4$
2009
Q138
JEE Mains
MCQ
10 Mar 2026
A motor cycle starts from rest and accelerates along a straight path at $2m/{s^2}.$ At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at $94\% $ of its value when the motor cycle was at rest? (Speed of sound $ = 330\,m{s^{ - 1}}$)
A.
$98$ $m$
B.
$147$ $m$
C.
$196\,m$
D.
$49$ $m$
2008
Q139
JEE Mains
MCQ
10 Mar 2026
While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of $18$ $cm$ during winter. Repeating the same experiment during summer, she measures the column length to be $x$ $cm$ for the second resonance. Then
A.
$18 > x$
B.
$x > 54$
C.
$54 > x > 36$
D.
$36 > x > 18$
2008
Q140
JEE Mains
MCQ
10 Mar 2026
A wave travelling along the $x$-axis is described by the equation $y(x, t)=0.005$ $\cos \,\left( {\alpha \,x - \beta t} \right).$ If the wavelength and the time period of the wave are $0.08$ $m$ and $2.0s$, respectively, then $\alpha $ and $\beta $ in appropriate units are
A.
$\alpha = 25.00\pi ,\,\beta = \pi $
B.
$\alpha = {{0.08} \over \pi },\,\beta = {{2.0} \over \pi }$
C.
$\alpha = {{0.04} \over \pi },\,\beta = {{1.0} \over \pi }$
D.
$\alpha = 12.50\pi ,\,\beta = {\pi \over {2.0}}$
2007
Q141
JEE Mains
MCQ
10 Mar 2026
A sound absorber attenuates the sound level by $20$ $dB$. The intensity decreases by a factor of
A.
$100$
B.
$1000$
C.
$10000$
D.
$10$
2006
Q142
JEE Mains
MCQ
10 Mar 2026
A string is stretched between fixed points separated by $75.0$ $cm.$ It is observed to have resonant frequencies of $420$ $Hz$ and $315$ $Hz$. There are no other resonant frequencies between these two. Then, the lowest resonant frequency for this string is
A.
$105$ $Hz$
B.
$1.05$ $Hz$
C.
$1050$ $Hz$
D.
$10.5$ $Hz$
2006
Q143
JEE Mains
MCQ
10 Mar 2026
A whistle producing sound waves of frequencies $9500$ $Hz$ and above is approaching a stationary person with speed $v$ $m{s^{ - 1}}.$ The velocity of sound in air is $300\,m{s^{ - 1}}.$ If the person can hear frequencies upto a maximum of $10,000$ $HZ,$ the maximum value of $v$ upto which he can hear whistle is
A.
$15\sqrt 2 \,\,m{s^{ - 1}}$
B.
${{15} \over {\sqrt 2 }}\,m{s^{ - 1}}$
C.
$15\,\,m{s^{ - 1}}$
D.
$30\,\,m{s^{ - 1}}$
2005
Q144
JEE Mains
MCQ
10 Mar 2026
An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency ?
A.
$0.5\% $
B.
zero
C.
$20\% $
D.
$5\% $
2005
Q145
JEE Mains
MCQ
10 Mar 2026
When two tuning forks (fork $1$ and fork $2$) are sounded simultaneously, $4$ beats per second are heated. Now, some tape is attached on the prong of the fork $2.$ When the tuning forks are sounded again, $6$ beats per second are heard. If the frequency of fork $1$ is $200$ $Hz$, then what was the original frequency of fork $2$ ?
A.
$202$ $Hz$
B.
$200$ $Hz$
C.
$204$ $Hz$
D.
$196$ $Hz$
2004
Q146
JEE Mains
MCQ
10 Mar 2026
The displacement $y$ of a particle in a medium can be expressed as, $y = {10^{ - 6}}\,\sin $ $\left( {100t + 20x + {\pi \over 4}} \right)$ $m$ where $t$ is in second and $x$ in meter. The speed of the wave is
A.
$20\,\,m/s$
B.
$5\,m/s$
C.
$2000\,m/s$
D.
$5\,\pi \,m/s$
2003
Q147
JEE Mains
MCQ
10 Mar 2026
A tuning fork of known frequency $256$ $Hz$ makes $5$ beats per second with the vibrating string of a piano. The beat frequency decreases to $2$ beats per second when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was
A.
$256 + 2Hz$
B.
$256 - 2Hz$
C.
$256 - 5Hz$
D.
$256 + 5Hz$
2003
Q148
JEE Mains
MCQ
10 Mar 2026
A metal wire of linear mass density of $9.8$ $g/m$ is stretched with a tension of $10$ $kg$-$wt$ between two rigid supports $1$ metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency $n.$ The frequency $n$ of the alternating source is
A.
$50$ $Hz$
B.
$100$ $Hz$
C.
$200$ $Hz$
D.
$25$ $Hz$
2003
Q149
JEE Mains
MCQ
10 Mar 2026
The displacement $y$ of a wave travelling in the $x$-direction is given by
$$y = {10^{ - 4}}\,\sin \left( {600t - 2x + {\pi \over 3}} \right)\,\,metres$$
where $x$ is expressed in metres and $t$ in seconds. The speed of the wave - motion, in $m{s^{ - 1}}$, is
where $x$ is expressed in metres and $t$ in seconds. The speed of the wave - motion, in $m{s^{ - 1}}$, is
A.
$300$
B.
$600$
C.
$1200$
D.
$200$
2002
Q150
JEE Mains
MCQ
10 Mar 2026
length of a string tied to two rigid supports is $40$ $cm$. Maximum length (wavelength in $cm$) of a stationary wave produced on it is
A.
$20$
B.
$80$
C.
$40$
D.
$120$
