Waves PYQs - Last 5 Years

A transverse wave on a string is described by $y=3 \sin (36 t+0.018 x+\pi / 4)$. where $x, y$ are in cm and $t$ in seconds. The least distance between the two successive crests in the wave is $\_\_\_\_$ cm . (Nearest integer)
$$ (\pi=3.14) ...

The equation of a plane progressive wave is given by $y = 5 \cos \pi \left( 200t - \frac{x}{150} \right)$ where $x$ and $y$ are in cm and $t$ is in second. The velocity of the wave is ________ m/s.

Two tuning forks A and B are sounded together giving rise to 8 beats in 2 s. When fork A is loaded with wax, the beat frequency is reduced to 4 beats in 2 s. If the original frequency of tuning fork B is 380 Hz then original frequency of tu...

The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is $5 / x$. The value of $x$ is $\_\_\_\_$

A point source is kept at the center of a spherically enclosed detector. If the volume of the detector increased by 8 times, the intensity will

The velocity of sound in air is doubled when the temperature is raised from $0^{\circ} \mathrm{C}$ to $\alpha{ }^{\circ} \mathrm{C}$. The value of $\alpha$ is $\_\_\_\_$ .

Two loudspeakers $\left(L_1\right.$ and $\left.L_2\right)$ are placed with a separation of 10 m , as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at po...

In an open organ pipe $\nu_3$ and $\nu_6$ are $3^{\text {rd }}$ and $6^{\text {th }}$ harmonic frequencies, respectively. If $\nu_6-\nu_3=2200 \mathrm{~Hz}$ then length of the pipe is $\_\_\_\_$ mm .
(Take velocity of sound in air is $330 \...

Two strings $(A, B)$ having linear densities $\mu_A=2 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ and, $\mu_B=4 \times 10^{-4} \mathrm{~kg} / \mathrm{m}$ and lengths $L_A=2.5 \mathrm{~m}$ and $L_B=1.5 \mathrm{~m}$ respectively are joined. Fre...

Two strings with circular cross section and made of same material, are stretched to have same amount of tension. A transverse wave is then made to pass through both the strings. The velocity of the wave in the first string having the radius...

The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, $y_1(x, t) = 4 \sin (kx - \omega t)$ and $y_2(x, t) = 2 \sin (kx - \omega t + \frac{2\pi}{3})$, are: (Take the angular frequency of init...

Two harmonic waves moving in the same direction superimpose to form a wave $x=\mathrm{a} \cos (1.5 \mathrm{t}) \cos (50.5 \mathrm{t})$ where t is in seconds. Find the period with which they beat. (close to nearest integer)

The equation of a wave travelling on a string is y = sin[20πx + 10πt], where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

In an experiment with a closed organ pipe, it is filled with water by $\left(\frac{1}{5}\right)$ th of its volume. The frequency of the fundamental note will change by

Displacement of a wave is expressed as $x(t)=5 \cos \left(628 t+\frac{\pi}{2}\right) \mathrm{m}$. The wavelength of the wave when its velocity is $300 \mathrm{~m} / \mathrm{s}$ is :
\((\pi=3.14)\)

In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is:

A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the $x$-direction in 0.3 sec . The crest P is at $x=0$ at $\mathrm{t}=0 \mathrm{sec}$ and maximum displacement of the wave is 2 cm . Which equation correctly represen...

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$
Assertion A: A sound wave has higher speed in solids than gases.
Reason R: Gases have higher value of Bulk modulus than solids....

The equation of a transverse wave travelling along a string is $y(x, t)=4.0 \sin \left[20 \times 10^{-3} x+600 t\right] \mathrm{mm}$, where $x$ is in mm and $t$ is in second. The velocity of the wave is :

A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities $\rho_1$ and $\rho_2$, respectively. The frequency of $9^{\text {th }}$ harmonic of closed tube is identical with $4^{\...

A closed and an open organ pipe have same lengths. If the ratio of frequencies of their seventh overtones is \(\left(\frac{a-1}{a}\right)\) then the value of \(a\) is _________.

A plane progressive wave is given by \(y=2 \cos 2 \pi(330 \mathrm{t}-x) \mathrm{m}\). The frequency of the wave is :

Two open organ pipes of lengths \(60 \mathrm{~cm}\) and \(90 \mathrm{~cm}\) resonate at \(6^{\text {th }}\) and \(5^{\text {th }}\) harmonics respectively. The difference of frequencies for the given modes is _________ \(\mathrm{Hz}\). (Vel...

A sonometer wire of resonating length \(90 \mathrm{~cm}\) has a fundamental frequency of \(400 \mathrm{~Hz}\) when kept under some tension. The resonating length of the wire with fundamental frequency of \(600 \mathrm{~Hz}\) under same tens...

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is \(60 \mathrm{~cm}\), the length of the closed pipe will be:

In a closed organ pipe, the frequency of fundamental note is \(30 \mathrm{~Hz}\). A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to \(110 \mathrm{~Hz}\). If the organ pipe has a cros...

A point source is emitting sound waves of intensity \(16 \times 10^{-8} \mathrm{~Wm}^{-2}\) at the origin. The difference in intensity (magnitude only) at two points located at a distances of \(2 m\) and \(4 m\) from the origin respectively...

A closed organ pipe \(150 \mathrm{~cm}\) long gives 7 beats per second with an open organ pipe of length \(350 \mathrm{~cm}\), both vibrating in fundamental mode. The velocity of sound is __________ \(\mathrm{m} / \mathrm{s}\).

A tuning fork resonates with a sonometer wire of length $1 \mathrm{~m}$ stretched with a tension of $6 \mathrm{~N}$. When the tension in the wire is changed to $54 \mathrm{~N}$, the same tuning fork produces 12 beats per second with it. The...

An organ pipe \(40 \mathrm{~cm}\) long is open at both ends. The speed of sound in air is \(360 \mathrm{~ms}^{-1}\). The frequency of the second harmonic is ___________ \(\mathrm{Hz}\).

The engine of a train moving with speed \(10 \mathrm{~ms}^{-1}\) towards a platform sounds a whistle at frequency \(400 \mathrm{~Hz}\). The frequency heard by a passenger inside the train is: (neglect air speed. Speed of sound in air $$=330...

A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be _________ cm.

A person driving car at a constant speed of \(15 \mathrm{~m} / \mathrm{s}\) is approaching a vertical wall. The person notices a change of \(40 \mathrm{~Hz}\) in the frequency of his car's horn upon reflection from the wall. The frequency o...

The displacement equations of two interfering waves are given by

$y_{1}=10 \sin \left(\omega t+\frac{\pi}{3}\right) \mathrm{cm}, y_{2}=5[\sin \omega t+\sqrt{3} \cos \omega t] \mathrm{cm}$ respectively.

The amplitude of the resultant wave ...

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is _________ degree.

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

The distance between two consecutive points with phase difference of 60\(^\circ\) in a wave of frequency 500 Hz is 6.0 m. The velocity with which wave is travelling is __________ km/s

A train blowing a whistle of frequency 320 Hz approaches an observer standing on the platform at a speed of 66 m/s. The frequency observed by the observer will be (given speed of sound = 330 ms\(^{-1}\)) __________ Hz.

A travelling wave is described by the equation
\(y(x,t) = [0.05\sin (8x - 4t)]\) m
The velocity of the wave is : [all the quantities are in SI unit]

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

The fundamental frequency of vibration of a string stretched between two rigid support is $50 \mathrm{~Hz}$. The mass of the string is $18 \mathrm{~g}$ and its linear mass density is $20 \mathrm{~g} / \mathrm{m}$. The speed of the transvers...

In an experiment with sonometer when a mass of \(180 \mathrm{~g}\) is attached to the string, it vibrates with fundamental frequency of \(30 \mathrm{~Hz}\). When a mass \(\mathrm{m}\) is attached, the string vibrates with fundamental freque...

For a certain organ pipe, the first three resonance frequencies are in the ratio of \(1:3:5\) respectively. If the frequency of fifth harmonic is \(405 \mathrm{~Hz}\) and the speed of sound in air is \(324 \mathrm{~ms}^{-1}\) the length of ...

The equation of wave is given by
\(\mathrm{Y}=10^{-2} \sin 2 \pi(160 t-0.5 x+\pi / 4)\)
where \(x\) and \(Y\) are in \(\mathrm{m}\) and \(\mathrm{t}\) in \(s\). The speed of the wave is ________ \(\mathrm{km} ~\mathrm{h}^{-1}\).

A car P travelling at \(20 \mathrm{~ms}^{-1}\) sounds its horn at a frequency of \(400 \mathrm{~Hz}\). Another car \(\mathrm{Q}\) is travelling behind the first car in the same direction with a velocity \(40 \mathrm{~ms}^{-1}\).

The freque...

A transverse harmonic wave on a string is given by
\(y(x,t) = 5\sin (6t + 0.003x)\)
where x and y are in cm and t in sec. The wave velocity is _______________ ms\(^{-1}\).

For a periodic motion represented by the equation
\(y=\sin \omega \mathrm{t}+\cos \omega \mathrm{t}\)
the amplitude of the motion is

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 kmh\(-\)1 in the direction of wind which is blowing at 72 kmh\(-\)1 speed. Frequency of siren is 720 ...

Which of the following equations correctly represents a travelling wave having wavelength \(\lambda\) = 4.0 cm, frequency v = 100 Hz and travelling in positive x-axis direction?

A longitudinal wave is represented by \(x = 10\sin 2\pi \left( {nt - {x \over \lambda }} \right)\) cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to :