Waves & Sound · JEE Main previous year questions

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle $60^{\circ }$ with ground level. But he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is :

1. A.$\frac{\sqrt{3}}{2}v$
2. B.$\frac{2v}{\sqrt{3}}$
3. C.$v$
4. D.$\frac{v}{2}$

A travelling harmonic wave is represented by the equation $y(x,t)=10^{-3}\sin (50t+2x)$, where, x and y are in metre and t is in seconds. Which of the following is a correct statement about the wave ?

1. A.The wave is propagating along the positive x-axis with speed $100\mathrm{m}{\mathrm{s}}^{-1}$
2. B.The wave is propagating along the positive x-axis with speed $25\mathrm{m}{\mathrm{s}}^{-1}$
3. C.The wave is propagating along the negative x-axis with speed $25\mathrm{m}{\mathrm{s}}^{-1}$
4. D.The wave is propagating along the negative x-axis with speed $100\mathrm{m}{\mathrm{s}}^{-1}$

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 :

1. A.$335\mathrm{m}{\mathrm{s}}^{-1}$
2. B.$328\mathrm{m}{\mathrm{s}}^{-1}$
3. C.$341\mathrm{m}{\mathrm{s}}^{-1}$
4. D.$322\mathrm{m}{\mathrm{s}}^{-1}$

A tuning fork vibrates with frequency $256Hz$ 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 $340m{s}^{-1}$)

1. A.$220cm$
2. B.$190cm$
3. C.$180cm$
4. D.$200cm$

1. A.$1:1$
2. B.$1:2$
3. C.$1:3$
4. D.$4:1$

An air column in a pipe, which is closed at one end, will be in resonance with a vibrating tuning fork of frequency $264\mathrm{Hz}$ if the length of the column in $\mathrm{cm}$ is (velocity of $\mathrm{sound}=330m/s$)

1. A.$125.00$
2. B.$93.75$
3. C.$62.50$
4. D.$187.50$

A wave represented by the equation $y_1=a\cos (kx-\omega t)$ is superimposed with another wave to form a stationary wave such that the point $x=0$ is node. The equation for the other wave is

1. A.$a\cos (kx-\omega t+\pi )$
2. B.$a\cos (kx+\omega t+\pi )$
3. C.$a\cos \left(kx+\omega t+\frac{\pi }{2}\right)$
4. D.$a\cos \left(kx-\omega t+\frac{\pi }{2}\right)$

Three sound waves of equal amplitudes have frequencies $(v-1)$, $v$, $(v+1)$. They superpose to give beats. The number of beats produced per second will be :

1. A.3
2. B.2
3. C.1
4. D.4

A whistle producing sound waves of frequencies $9500\mathrm{Hz}$ and above is approaching a stationary person with speed $v\mathrm{m}{\mathrm{s}}^{-1}$. The velocity of sound in air is $300\mathrm{m}{\mathrm{s}}^{-1}$. If the person can hear frequencies upto a maximum of $10,000\mathrm{HZ}$, the maximum value of $v$ upto which he can hear whistle is

1. A.$15\sqrt{2}\mathrm{m}{\mathrm{s}}^{-1}$
2. B.$\frac{15}{\sqrt{2}}\mathrm{m}{\mathrm{s}}^{-1}$
3. C.$15\mathrm{m}{\mathrm{s}}^{-1}$
4. D.$30\mathrm{m}{\mathrm{s}}^{-1}$

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 $200\mathrm{Hz}$, then what was the original frequency of fork 2 ?

1. A.$202\mathrm{Hz}$
2. B.$200\mathrm{Hz}$
3. C.$204\mathrm{Hz}$
4. D.$196\mathrm{Hz}$

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 ?

1. A.$0.5\%$
2. B.$\mathrm{zero}$
3. C.$20\%$
4. D.$5\%$

A tuning fork arrangement (pair) produces $4$ beats/sec with one fork of frequency $288\mathrm{cps}$. A little wax is placed on the unknown fork and it then produces $2$ beats/sec. The frequency of the unknown fork is

1. A.$286\mathrm{cps}$
2. B.$292\mathrm{cps}$
3. C.$294\mathrm{cps}$
4. D.$288\mathrm{cps}$

When temperature increases, the frequency of a tuning fork

1. A.increases
2. B.decreases
3. C.remains same
4. D.increases or decreases depending on the material