Waves Questions

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

Sound waves travel at $350\text{m/s}$ through warm air and at $3500\text{m/s}$ through brass. The wavelength of a $700\text{Hz}$ acoustic wave as it enters brass from warm air:

Two waves are represented by the equations $y_1=a\sin (\omega t+kx+0.57)\text{m}$ and $y_2=a\cos (\omega t+kx)\text{m}$. The phase difference between them is:

The number of possible natural oscillations of 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 $=340{\text{ms}}^{-1}$)

When a string is divided into three segments of length $l_1,l_2$ and $l_3$, the fundamental frequencies of these three segments are ${\nu }_1,{\nu }_2$ and ${\nu }_3$ respectively. The original fundamental frequency ($\nu$) of the string is:

Two sources of sound placed close to each other, are emitting progressive waves given by $y_1=4\sin 600\pi t$ and $y_2=5\sin 608\pi t$. An observer located near these two sources of sound will hear:

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

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

A source of unknown frequency $f_u$ gives $4\text{beats/s}$ with a known source of $250\text{Hz}$. The second harmonic of $f_u$ ($2f_u$) gives $5\text{beats/s}$ with a source of $513\text{Hz}$. The unknown frequency 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 equation of a simple harmonic wave is given by $y=3\sin \frac{\pi }{2}(50t-x)$. The ratio of maximum particle velocity to the wave velocity is:

A speeding motorcyclist sees traffic jam ahead of him. He slows down to $36\text{km/hour}$. He finds that traffic has eased and a car moving ahead of him at $18\text{km/hour}$ is honking at a frequency of $1392\text{Hz}$. If the speed of sound is $343\text{m/s}$, the frequency of the honk as heard by him 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 $19.4{\text{ms}}^{-1}$ at an angle of $60^{\circ }$ with the source-observer line. 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:

A siren emitting a sound of frequency $800\text{Hz}$ moves away from an observer towards a cliff at a speed of $15{\text{ms}}^{-1}$. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is: (Take velocity of sound in air $=330{\text{ms}}^{-1}$)

An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is $50\text{cm}$. The next larger length of the column resonating with the same tuning fork is:

A uniform rope of length $L$ and mass $m_1$, hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength ${\lambda }_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is ${\lambda }_2$. The ratio ${\lambda }_2/{\lambda }_1$ is:

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

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

A train moving at $220{\text{ms}}^{-1}$ towards an object emits $1000\text{Hz}$ sound. Some sound reflects back as an echo. The frequency of the echo detected by the driver is: ($v_s=330{\text{ms}}^{-1}$)

Two wires under tension $T$ have frequency $600\text{Hz}$. Fractional increase in tension of one to produce $6\text{beats/s}$ is:

Which of the following statements is false for the properties of electromagnetic waves?

A tuning fork of frequency $512\text{ Hz}$ makes $4\text{ beats per second}$ with the vibrating string of a piano. The beat frequency decreases to $2\text{ beats per sec}$ when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was:

A transverse wave is represented by $y=A\sin (\omega t-kx)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

The electric field part of an electromagnetic wave in a medium is represented by $E_x=0$, $E_y=2.5\text{N/C}\cos [2\pi \times 10^6\frac{\text{rad}}{\text{s}}t-\pi \times 10^{-2}\frac{\text{rad}}{\text{m}}x]$, $E_z=0$. The wave is:

A wave in a string has an amplitude of $2\text{cm}$. The wave travels in the $+ve$ direction of $x$ axis with a speed of $128\text{m/sec}$ and it is noted that $5$ complete waves fit in $4\text{m}$ length of the string. The equation describing the wave is:

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

Each of the two strings of length $51.6\text{cm}$ and $49.1\text{cm}$ are tensioned separately by $20\text{N}$ force. Mass per unit length of both the strings is same and equal to $1\text{g/m}$. When both the strings vibrate simultaneously, the number of beats is:

Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is:

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

The wave described by $y=0.25\sin (10\pi x-2\pi t)$, where $x$ and $y$ are in meters and $t$ in seconds, is a wave travelling along the:

The time of reverberation of a room A is one second. What will be the time (in seconds) of reverberation of a room, having all the dimensions double of those of room A ?

A transverse wave propagating along x-axis is represented by:$y(x,t)=8.0\sin (0.5\pi x-4\pi t-\frac{\pi }{4})$ Where $x$ is in meters and $t$ is in seconds. The speed of the wave is :

Two sound waves with wavelength $5.0\text{m}$ and $5.5\text{m}$ respectively, each propagates in gas with a velocity of $330\text{m/s}$. We expect the following number of beats per seconds: