Waves & Sound · JEE Main previous year questions

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

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

A steel wire with mass per unit length $7.0\times 10^{-3}{\text{ kg m}}^{-1}$ is under tension of $70\text{ N}$. The speed of transverse waves in the wire will be:

1. A.$10\text{ m/s}$
2. B.$50\text{ m/s}$
3. C.$100\text{ m/s}$
4. D.$200\pi \text{ m/s}$

A person observes two moving trains, 'A' reaching the station and 'B' leaving the station with equal speed of $30m/s$. If both trains emit sounds with frequency $300\mathrm{Hz}$, (Speed of sound: $330m/s$) approximate difference of frequencies heard by the person will be:

1. A.10 Hz
2. B.55 Hz
3. C.80 Hz
4. D.33 Hz

An employee of a factory moving away from his workplace by a car listens to the siren of the factory. He drives the car at the speed of $72{\text{ kmh}}^{-1}$ in the direction of wind which is blowing at $72{\text{ kmh}}^{-1}$ speed. Frequency of siren is $720\text{ Hz}$. The employee hears an apparent frequency of ___________ Hz. (Assume speed of sound to be $340{\text{ ms}}^{-1}$)

A tuning fork of frequency $340\mathrm{Hz}$ resonates in the fundamental mode with an air column of length $125\mathrm{cm}$ in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ____ $\mathrm{cm}$. (Velocity of sound in air is $340\mathrm{m}{\mathrm{s}}^{-1}$)

An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be :

1. A.20%
2. B.10%
3. C.5%
4. D.0%

A set of 20 tuning forks is arranged in a series of increasing frequencies. If each fork gives 4 beats with respect to the preceding fork and the frequency of the last fork is twice the frequency of the first, then the frequency of last fork is _________ Hz.

The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is _____________ cm.

The frequency of a car horn encountered a change from 400 Hz to 500 Hz, when the car approaches a vertical wall. If the speed of sound is 330 m/s. Then the speed of car is ___________ km/h.

The mass per unit length of a uniform wire is 0.135 g/cm. A transverse wave of the form $y=-0.21\sin (x+30t)$ is produced in it, where x is in meter and t is in second. Then, the expected value of tension in the wire is $x\times 10^{-2}\mathrm{N}$. Value of x is _________. (Round off to the nearest integer)

A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency 340 Hz. When fork A is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A?

1. A.335 Hz
2. B.345 Hz
3. C.338 Hz
4. D.342 Hz

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

Three harmonic waves having equal frequency $\nu$ and same intensity $I_0$, have phase angles $0$, $\frac{\pi }{4}$ and $-\frac{\pi }{4}$ respectively. When they are superimposed the intensity of the resultant wave is close to :

1. A.$5.8I_0$
2. B.$3I_0$
3. C.$0.2I_0$
4. D.$I_0$

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 is 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.

A transverse wave travels on a taut steel wire with a velocity of v when tension in it is $2.06\times 10^4\text{ N}$. When the tension is changed to T, the velocity changed to v/2. The value of T is close to :

1. A.$30.5\times 10^4\text{ N}$
2. B.$2.50\times 10^4\text{ N}$
3. C.$10.2\times 10^2\text{ N}$
4. D.$5.15\times 10^3\text{ N}$

A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears 2 beats/sec. The oscillation frequency of each tuning fork is ${\nu }_0=1400\text{ Hz}$ and the velocity of sound in air is $350\text{ m/s}$. The speed of each tuning fork is close to :

1. A.1 m/s
2. B.$\frac{1}{8}\text{ m/s}$
3. C.$\frac{1}{4}\text{ m/s}$
4. D.$\frac{1}{2}\text{ m/s}$

1. A.$\frac{\pi }{2}$
2. B.$\pi$
3. C.0
4. D.$-\frac{\pi }{2}$

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 =$1500{\text{ ms}}^{-1}$)

1. A.507 Hz
2. B.502 Hz
3. C.499 Hz
4. D.504 Hz

A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound (v) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, $l_1=30\text{ cm}$ and $l_2=70\text{ cm}$. Then, v is equal to -

1. A.$338{\text{ ms}}^{-1}$
2. B.$384{\text{ ms}}^{-1}$
3. C.$379{\text{ ms}}^{-1}$
4. D.$332{\text{ ms}}^{-1}$

A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120 dB intensity sound ? [Given reference intensity of sound as $10^{-12}{\text{ W/m}}^2$]

1. A.20 cm
2. B.10 cm
3. C.40 cm
4. D.30 cm

Two sources of sound $S_1$ and $S_2$ produce sound waves of same frequency 660 Hz. A listener is moving from source $S_1$ towards $S_2$ with a constant speed u m/s and he hears 10 beats/s. The velocity of sound is 330 m/s. Then, u equals :

1. A.10.0 m/s
2. B.5.5 m/s
3. C.15.0 m/s
4. D.2.5 m/s

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)

1. A.12, 18
2. B.16, 14
3. C.12, 16
4. D.8, 18

The pressure wave, $P=0.01\sin [1000t-3x]\mathrm{N}{\mathrm{m}}^{-2}$, 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 $336\mathrm{m}{\mathrm{s}}^{-1}$. Approximate value of T is

1. A.12°C
2. B.15°C
3. C.4°C
4. D.11°C

A string is clamped at both the ends and it is vibrating in its 4th harmonic. The equation of the stationary wave is $Y=0.3\sin (0.157x)\cos (200\pi t)$. The length of the string is : (All quantities are in SI units.)

1. A.60 m
2. B.20 m
3. C.80 m
4. D.40 m

Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of $20\mathrm{m}{\mathrm{s}}^{-1}$ 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 $=340\mathrm{m}{\mathrm{s}}^{-1}$) :-

1. A.2300 Hz
2. B.2060 Hz
3. C.2250 Hz
4. D.2150 Hz