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Waves

194 Questions
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2019 JEE Mains MCQ
JEE Main 2019 (Online) 10th April Evening Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 10th April Evening Slot
The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies 9 Hz and 11 Hz, is :
A.
JEE Main 2019 (Online) 10th April Evening Slot Physics - Waves Question 102 English Option 1
B.
JEE Main 2019 (Online) 10th April Evening Slot Physics - Waves Question 102 English Option 2
C.
JEE Main 2019 (Online) 10th April Evening Slot Physics - Waves Question 102 English Option 3
D.
JEE Main 2019 (Online) 10th April Evening Slot Physics - Waves Question 102 English Option 4
2019 JEE Mains MCQ
JEE Main 2019 (Online) 10th April Morning Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 9th April Evening Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 9th April Evening Slot
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) :-
A.
2300 Hz
B.
2060 Hz
C.
2250 Hz
D.
2150 Hz
2019 JEE Mains MCQ
JEE Main 2019 (Online) 9th April Morning Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 9th April Morning Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 8th April Morning Slot
JEE Main 2019 (Online) 8th April Morning Slot Physics - Waves Question 108 English 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 JEE Mains MCQ
JEE Main 2019 (Online) 12th January Evening Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 12th January Morning Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 11th January Morning Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 10th January Morning Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 10th January Morning Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 9th January Evening Slot
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 JEE Mains MCQ
JEE Main 2019 (Online) 9th January Morning Slot
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 JEE Mains MCQ
JEE Main 2018 (Online) 16th April Morning Slot
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 JEE Mains MCQ
JEE Main 2018 (Online) 16th April Morning Slot
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 JEE Mains MCQ
JEE Main 2018 (Offline)
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 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Evening Slot
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 JEE Mains MCQ
JEE Main 2018 (Online) 15th April Morning Slot
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 JEE Mains MCQ
JEE Main 2017 (Online) 9th April Morning Slot
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.)
A.
160 m/s
B.
90 m/s
C.
180 m/s
D.
120 m/s
2017 JEE Mains MCQ
JEE Main 2017 (Online) 9th April Morning Slot
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 JEE Mains MCQ
JEE Main 2017 (Online) 8th April Morning Slot
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 :

JEE Main 2017 (Online) 8th April Morning Slot Physics - Waves Question 120 English
A.
1 : 1
B.
1 : 2
C.
1 : 3
D.
4 : 1
2017 JEE Mains MCQ
JEE Main 2017 (Offline)
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 JEE Mains MCQ
JEE Main 2016 (Online) 10th April Morning Slot
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 JEE Mains MCQ
JEE Main 2016 (Online) 9th April Morning Slot
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 JEE Mains MCQ
JEE Main 2016 (Offline)
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 ${\,\,g = 10m{s^{ - 2}}}$ )
A.
$2\sqrt 2 s$
B.
$2\pi \sqrt 2 s$
C.
$2\pi \sqrt 2 s$
D.
$2$ $s$
2016 JEE Mains MCQ
JEE Main 2016 (Offline)
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 JEE Mains MCQ
JEE Main 2015 (Offline)
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 JEE Mains MCQ
JEE Main 2014 (Offline)
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 JEE Mains MCQ
JEE Main 2013 (Offline)
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 JEE Mains MCQ
AIEEE 2012
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 JEE Mains MCQ
AIEEE 2011
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 JEE Mains MCQ
AIEEE 2010
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 JEE Mains MCQ
AIEEE 2009
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 JEE Mains MCQ
AIEEE 2009
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 JEE Mains MCQ
AIEEE 2008
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 JEE Mains MCQ
AIEEE 2008
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 JEE Mains MCQ
AIEEE 2007
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 JEE Mains MCQ
AIEEE 2006
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 JEE Mains MCQ
AIEEE 2006
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 JEE Mains MCQ
AIEEE 2005
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 JEE Mains MCQ
AIEEE 2005
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 JEE Mains MCQ
AIEEE 2004
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 JEE Mains MCQ
AIEEE 2003
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 JEE Mains MCQ
AIEEE 2003
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 JEE Mains MCQ
AIEEE 2003
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
A.
$300$
B.
$600$
C.
$1200$
D.
$200$
2002 JEE Mains MCQ
AIEEE 2002
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.
$120$
2002 JEE Mains MCQ
AIEEE 2002
A wave $y=a$ $\sin \left( {\omega t - kx} \right)$ on a string meets with another wave producing a node at $x=0.$ Then the equation of the unknown wave is
A.
$y = a\,\sin \,\left( {\omega t + kx} \right)$
B.
$y = - a\,\sin \,\left( {\omega t + kx} \right)$
C.
$y = a\,\sin \,\left( {\omega t - kx} \right)$
D.
$y = - a\,\sin \,\left( {\omega t - kx} \right)$
2002 JEE Mains MCQ
AIEEE 2002
When temperature increases, the frequency of a tuning fork
A.
increases
B.
decreases
C.
remains same
D.
increases or decreases depending on the material