Waves PYQs

For a travelling harmonic wave y(x,t)=2.0 cos 2π(10t−0.0080x+0.35), where x and y are in cm and t in s. The phase difference between oscillatory motion of two points separated by a distance of 0.5 m is:

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is :

If the tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is

In a guitar, two strings A and B made of same material are slightly out of tune and produce beats of frequency 6 Hz. When tension in B is slightly decreased, the beat frequency increases to 7 Hz. If the frequency of A is 530 Hz, the original frequency of B will be :

A tuning fork with frequency 800 Hz produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Successive resonances are observed at lengths 9.75 cm, 31.25 cm and 52.75 cm. The speed of sound in air is:

A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of 27°C two successive resonances are obtained at 20 cm and 73 cm column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27°C is:

The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is:

The two nearest harmonics of a tube closed at one end and open at the other end are $220\,\text{Hz}$ and $260\,\text{Hz}$. What is the fundamental frequency of the system?

Two cars moving in opposite directions approach each other with speeds of $22\,\text{m/s}$ and $16.5\,\text{m/s}$ respectively. The driver of the first car blows a horn having frequency $400\,\text{Hz}$. The frequency heard by the driver of the second car is: (Velocity of sound $= 340\,\text{m/s}$)

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe of length $L$. The length of the open pipe will be:

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

A source of sound $S$ emitting waves of frequency $100\,\text{Hz}$ and an observer $O$ are located at some distance from each other. The source is moving with a speed of $19.4\,\text{m s}^{-1}$ at an angle of $60^{\circ}$ with the source-observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air $330\,\text{ms}^{-1}$) is:

A string is stretched between fixed points separated by $75.0\,\text{cm}$. It is observed to have resonant frequencies of $420\,\text{Hz}$ and $315\,\text{Hz}$. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is:

If $n_1$, $n_2$ and $n_3$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by:

The number of possible natural oscillations of an air column in a pipe closed at one end of length $85\,\text{cm}$ whose frequencies lie below $1250\,\text{Hz}$ are: (velocity of sound = 340 ms⁻¹)

A speeding motorcyclist sees traffic jam ahead of him. He slows down to 36 km/hour. He finds that traffic has eased and a car moving ahead of him at 18 km/hour is honking at a frequency of 1392 Hz. If the speed of sound is 343 m/s, the frequency of the horn as heard by him will be:

A wave travelling in the positive x-direction having displacement along y-direction as $1\,m$, wavelength $2\pi\,m$ and frequency $\dfrac{1}{\pi}\,Hz$ is represented by

If we study the vibration of a pipe open at both ends, then the following statement is not true

A source of unknown frequency gives $4$ beats/s, when sounded with a source of known frequency $250\,\text{Hz}$. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency $513\,\text{Hz}$. The unknown frequency is

A train moving at a speed of 220 ${m s}^{-1}$ towards a stationary object emits a sound of frequency $1000\,\text{Hz}$. Some of the sound reaching the object gets reflected back to the train as echo. The frequency of the echo as detected by the driver of the train is: (Speed of sound in air is 330 ${m s}^{-1}$)

The equation of simple harmonic wave is given by: $$y=3\sin\left[\frac{\pi}{2}(50t-x)\right]$$ where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity is:

Two identical piano wires kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which would lead to occurrence of 6 beats/second when both the wires oscillate together would be:

The driver of a car traveling with speed $30\,\mathrm{m/s}$ towards a hill sounds a horn of frequency $600\,\mathrm{Hz}$. If the speed of sound in air is $330\,\mathrm{m/s}$, the frequency of reflected sound heard by the driver is:

A wave in a string has amplitude $2\,cm$. The wave travels in the positive $x$-direction with speed $128\,m/s$ and 5 complete waves are present in a length of $4\,m$. The equation describing the wave is:

Each of the two strings of lengths $51.6\,cm$ and $49.1\,cm$ are tensioned separately by $20\,N$. Mass per unit length of both strings is $1\,g/m$. When both strings vibrate simultaneously, the number of beats produced is:

The wave described by y = 0.25 sin(10πx − 2πt) where x and y are in meters and t in seconds, is a wave travelling along the

Two points are located at a distance of 10 m and 15 m from the source of oscillation. The period of oscillation is 0.05 s and the velocity of the wave is 300 m/s. What is the phase difference between the oscillations of the two points?

Two periodic waves of intensities I₁ and I₂ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

Equation for two waves is given as y₁ = a sin(ωt + φ₁), y₂ = a sin(ωt + φ₂). If amplitude and time period of resultant wave do not change, then calculate (φ₁ − φ₂).

Two stretched wires each produce a frequency of 500 Hz. By what percentage should the tension in one wire be increased so that 5 beats per second are heard?

A string having tension 360 N and mass per unit length 4 × 10⁻³ kg/m produces two consecutive resonant frequencies with a tuning fork, which are 375 Hz and 450 Hz. Find the mass of the string.

Two sound waves with wavelengths 5.0 m and 5.5 m respectively each propagate in a gas with velocity 330 m/s. We expect the following number of beats per second:

A transverse wave propagating along the x-axis is represented by y(x,t) = 8.0 sin(0.5πx − 4πt − π/4), where x is in metres and t is in seconds. The speed of the wave is:

Which one of the following statements is true?

Two vibrating tuning forks produce progressive waves given by y₁ = 4 sin 500πt and y₂ = 2 sin 506πt. Number of beats produced per minute is: