Waves PYQs - Last 5 Years

When source of sound and observer both are moving towards each other, the observer will hear

The fundamental frequency of a sonometer wire is 50 Hz for some length and tension. If the length is increased by $25 \%$ by keeping tension same then frequency change of second harmonic is

In a pipe closed at one end, air column is vibrating in its second overtone. The column has

A pipe open at both ends of length 1.5 m is dipped in water at one end such that $2^{\text {nd }}$ overtone of vibrating air column is resonating with a tuning fork of frequency 330 Hz . The length of the pipe immersed in water is (Speed of...

An observer on sea-coast counts 45 waves in one minute. If the wavelength of the waves is 7 m , then the velocity of the waves will be

Two sources of sound are emitting progressive waves $\mathrm{y}_1=4 \sin 710 \pi \mathrm{t}$ and $\mathrm{y}_2=3 \sin 702 \pi \mathrm{t}$. The sources are placed close to each other. The number of beats heard per second and intensity ratio ...

Two uniform wires of same material are vibrating under the same tension. If the $1^{\text {st }}$ overtone of $1^{\text {st }}$ wire is equal to the $2^{\text {nd }}$ overtone of $2^{\text {nd }}$ wire and radius of $1^{\text {st }}$ wire i...

A transverse displacement of vibrating string is $y=0.06 \sin \left(\frac{2 \pi}{3}\right) \times \cos (120 \pi t)$.
If the mass per unit length of a string is $4 \times 10^{-2} \mathrm{~kg} / \mathrm{m}$, then the tension in the string wil...

Two strings ' X ' and ' Y ' of a guitar produces a beat frequency of 6 Hz . When the tension of the string ' Y ' is increased, the beat frequency is found to be 4 Hz . If the frequency of string ' X ' is 300 Hz , then the original frequency...

A vehicle starts from rest and accelerates along straight path at $2 \mathrm{~m} / \mathrm{s}^2$. At the starting point of the vehicle, there is a stationary electric siren. How far has the vehicle nearly gone when the driver hears the sire...

The equation of a progressive wave is $\mathrm{Y}=3 \sin \left[\pi\left(\frac{\mathrm{t}}{3}-\frac{\mathrm{x}}{5}\right)+\frac{\pi}{4}\right]$ where x and y are in meter and time in second. Which of the following is correct?

A wire of length L , diameter ' d ' density of material ' e ' is under tension ' T ', having fundamental frequency of vibration $\mathrm{n}_{\mathrm{A}}$. Another wire of length 2 L , tension 2 T , density 2 e and diameter 3 d has fundament...

Two pipes of lengths $\mathrm{L}_1$ and $\mathrm{L}_2$, open at both ends are joined in series. If ' $f_1$ ' and ' $f_2$ ' are the fundamental frequencies of two pipes, then the fundamental frequency of series combination will be (neglect e...

When an observer moves towards a stationary source with velocity ' $\mathrm{V}_1$ ', the apparent frequency of emitted note is ' $\mathrm{F}_1$ '. When observer moves away from stationary source with velocity ' $\mathrm{V}_1$ ' the apparent...

In fundamental mode, the time required for the sound wave to reach up to closed end of a pipe filled with air is ' $t$ ' second. The frequency of vibration of air column is (Neglect end correction)

The closed and open organ pipe have same length and when they are vibrating simultaneously in first overtone produce 3 beats. The length of open pipe is made $\left(\frac{1}{3}\right)^{\mathrm{rd}}$ and that of closed pipe is made 3 times t...

The length of closed and open pipe is same. The ratio of frequency of $\mathrm{n}^{\text {th }}$ overtone for closed pipe to that of open pipe is (Neglect end correction)

The frequency of a stretched uniform wire of length $L$ under tension is in resonance with the fundamental frequency of a closed pipe of same length. If the tension in the wire is increased by 8 N , it is in resonance with the first overton...

The fundamental frequency of a closed pipe of length $L$ is equal to the second overtone of a pipe open at both the ends of length (XL). The value of X is (Neglect end correction)

A string of mass $0.1 \mathrm{kgm}^{-1}$ has length 0.9 m . It is fixed at both ends and stretched such that it has a tension of 40 N . The string vibrates in three segments with amplitude 0.3 cm . The amplitude (maximum) of the particle ve...

When source of sound moves towards a stationary observer, the apparent frequency heard by him

The frequency of fourth overtone of a closed pipe is in unison with the fifth overtone of an open pipe. The ratio of length of closed pipe to that of open pipe is

The frequency of a tuning fork is 256 Hz . It will not resonate with the tuning fork of frequency

In an organ pipe closed at one end; the sum of the frequencies of first three overtones is 3930 Hz . The frequency of the fundamental mode of organ pipe is

When two tuning forks are sounded together, 6 beats per second are heard. One of the fork is in unison with 0.70 m length of sonometer wire and another fork is in unison with 0.69 m length of the same sonometer wire. The frequencies of the ...

A progressive wave of frequency 400 Hz is travelling with velocity $336 \mathrm{~m} / \mathrm{s}$. How far apart are the two points on a wave which are $60^{\circ}$ out of phase?

A sonometer wire is stretched by hanging a metal bob, the fundamental frequency of the wire is ' $n_1$ '. When the bob is completely immersed in water, the frequency of vibration of wire becomes ' $n_2$ '. The relative density of the metal ...

Two sound waves having same amplitude ' $A$ ' and angular frequency ' $\omega$ ' but having a phase difference of $\left(\frac{\pi}{2}\right)^c$ are superimposed then the maximum amplitude of the resultant wave is

When the tension in string is increased by $3 \mathrm{~kg} \omega \mathrm{t}$, the frequency of the fundamental mode increases in the ratio $2: 3$. The initial tension in the string is

A tuning fork of frequency 340 Hz is vibrated just above a tube of 120 cm height. Water is slowly poured in the tube. What is the minimum height of water necessary for resonance?

Out of the following musical instruments, which is 'NOT' a percussion instrument?

The diagram shows the propagation of a progressive wave. A, B, C, D, E are five points on this wave

Which of the following points are in the same state of vibration?

A stationary wave is formed having 3 nodes along the length of the string 90 cm . The wavelength of the wave is

A string of mass 0.2 Kg is under a tension of 2.5 N . The length of the string is 2 m. A transverse wave starts from one end of the string. The time taken by the wave to reach the other end is

A musical instrument ' $P$ ' produces sound waves of frequency ' $n$ ' and amplitude ' $A$ '. Another musical instrument ' $Q$ ' produces sound waves of frequency $\frac{\mathrm{n}}{4}$. The waves produced by ' $P$ ' and ' $Q$ ' have equal ...

A sonometer wire is in unison with a tuning fork of frequency ' $n$ ' when it is stretched by a weight of specific gravity ' $d$ '. When the weight is completely immersed in water, ' $x$ ' beats are produced per second, then

The equations of two waves are given as
$$\begin{aligned} & y_1=a \sin \left(\omega t+\phi_1\right) \\ & y_2=a \sin \left(\omega t+\phi_2\right) \end{aligned}$$
If amplitude and time period of resultant wave is same as the individual waves,...

Two waves $\mathrm{Y}_1=0.25 \sin 316 \mathrm{t} \quad$ and $\mathrm{Y}_2=0.25 \sin 310 \mathrm{t}$ are propagating along the same direction. The number of beats produced per second are

The distance between two consecutive points with phase difference of $60^{\circ}$ in wave of frequency 500 Hz is 0.6 m . The velocity with which wave is travelling is

A progressive wave of frequency 400 Hz is travelling with a velocity $336 \mathrm{~m} / \mathrm{s}$. How far apart are the two points which are $60^{\circ}$ out of phase?

A string A has twice the length, twice the diameter, twice the tension and twice the density of another string B. The overtone of A which will have the same fundamental frequency as that of $B$ is

A transverse wave travelling along a stretched string has a speed of $30 \mathrm{~m} / \mathrm{s}$ and a frequency of 250 Hz . The phase difference between two points on the string 10 cm apart at the same instant is

A stationery wave is represented by $y=12 \cos \left(\frac{\pi}{6} x\right) \sin (8 \pi t)$, where $x & y$ are in cm and $t$ in second. The distance between two successive antinodes is

A train sounding a whistle of frequency 510 Hz approaches a station at $72 \mathrm{~km} / \mathrm{hr}$. The frequency of the note heard by an observer on the platform as the train (1) approaches the station and then (2) recedes the station ...

A set of 28 turning forks is arranged in an increasing order of frequencies. Each fork produces ' $x$ ' beats per second with the preceding fork and the last fork is an octave of the first. If the frequency of the $12^{\text {th }}$ fork is...

The displacement of a wave is given by $y=0.002 \sin (100 t+x)$ where ' $x$ 'and ' $y$ ' are in metre and ' $t$ ' is in second. This represents a wave

The pitch of a whistle of an engine appears to drop by $30 \%$ of original value when it passes a stationary observer. If the speed of sound in air is $350 \mathrm{~ms}^{-1}$, then the speed of engine in $\mathrm{ms}^{-1}$ is

The fundamental frequency of an air column in a pipe open at both ends is ' $\mathrm{f}_1$ '. Now $80 \%$ of its length is immersed in water, the fundamental frequency of the air column becomes $f_2$. The ratio of $f_1: f_2$ is

The path difference between two waves $\mathrm{Y}_1=\mathrm{a}_1 \sin \left(\omega \mathrm{t}-\frac{2 \pi \mathrm{x}}{\lambda}\right)$ and $\mathrm{Y}_2=\mathrm{a}_2 \cos \left(\omega \mathrm{t}-\frac{2 \pi \mathrm{x}}{\lambda}+\phi\right)$...

An observer moves towards a stationary source of sound with a velocity of one-fifth of the velocity of sound. The percentage increase in the apparent frequency is