Waves practice · Mixed difficulty

The displacement $y$ of a particle on a straight line is given by $y=f(x, t)$, as a function of time. Which of the following functions does not represent wave motion?

To decrease the fundamental frequency of a stretched string fixed at both ends. Which of the following option is correct?

‘SONAR’ emits which of the following waves

A resonance tube of (closed organ pipe) air column of length 20 cm resonates with a tuning fork of frequency 250 Hz. The speed of sound in air is [in $m{s^{ - 1}}]$

A cylindrical tube, closed at one end, has a fundamental frequency f in air. The $\frac{1}{4}th$ of the tube is filled with water. The fundamental frequency of the air column is now

The instantaneous displacement of a simple harmonic oscillator is given by $= a\,\,\,\cos \left[ {\omega t + \frac{\pi }{4}} \right]$. Its speed will be maximum at the time

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

The displacement of particles in a string stretched in the $x$ direction is represented by $y$. Among the following expressions for $y$, those describing wave motion are :

A travelling wave reflected at an open boundary undergoes a phase change of

If two coherent waves are represented by ${y_1} = 4\sin \omega t$ and ${y_2} = 3\sin \left( {\omega t + \pi /3} \right)$ interfere at a point, the amplitude of resulting wave will be about

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

Assertion(A): Speed of sound in $\mathrm{O}_2$ gas at temperature $T$ is $v$. If temperature is increased to $2 T$, the molecular oxygen breaks into atomic oxygen. Then, speed of sound under these conditions will become $2 v$.

Reason(R): With increase in humidity in air, speed of sound increases.

A string of length $1 \mathrm{~m}$ and mass $5 \mathrm{~g}$ is fixed at both ends. The tension in the string is $8.0 \mathrm{~N}$. The string is set into vibration using an external vibrator of frequency $100 \mathrm{~Hz}$. The separation between successive nodes on the string in $\mathrm{cm}$ is close to

Two tuning fork, $A$ and $B$ produce notes of frequencies $258\,\,Hz$ and $262\,\,Hz$. An unknown note sounded with a produces certain beats. When the same note is sounded with $B$, the beat frequency gets doubled, the unknown frequency is

A tuning fork $A$ of frequency 512 Hz produce 5 beats/sec. When sounded with another tuning fork $B$ of unknown frequency. If $B$ is loaded with wax the numbers of beats is again 5 beats/second. The frequency of tuning fork $B$ before it was loaded is:

A travelling wave is produced on a long horizontal string by vibrating an end up and down sinusoidally. The amplitude of vibration is $1.0 \mathrm{~cm}$ and the displacement becomes zero 200 times per second. The linear mass density of the string is $0.10 \mathrm{~kg} \mathrm{~m}^{-1}$ and it is kept under a tension of 90 N. Find the velocity and acceleration of the particle at $x=50 \mathrm{~cm}$ at time $t=10 \mathrm{~ms}$.

The speed sound in air is 332 m/s. The speed of sound in air in units of km per hour will be

Speed of sound at constant temperature depends on

The wave function of a pulse is given by $y=\frac{3}{(2 x+3 t)^2}$ where $x$ and $y$ are in metre and $t$ is in second.

i) Identify the direction of propagation.

ii) Determine the wave velocity of the pulse.

If fundamental frequency is 50 and next successive frequencies are 150 and 250 then it is

The phase difference between the two given waves is ${y_1} = {a_1}\sin \left( {\omega t - \frac{{2\pi }}{\lambda }X} \right)\,\,\,{y_2} = {a_2}\cos \left( {\omega t - \frac{{2\pi }}{\lambda }X + \phi } \right)\,$

A source of sound gives $5$ beats ${\mathrm{s}^{ - 1}}$ when sounded with another source of frequency $100\,\,Hz$. The second harmonic of the source together with a source of frequency $205\,\,Hz$ gives $5\,\,beats\,\,{s^{( - 1)}}$. What is the frequency of the source?

Assertion: For same length but different gas COP fundamental frequency are different.
Reason: Here frequency is proportional to velocity for same length given.

On the superposition of two harmonic oscillations represented by ${X_1} = a\sin \left( {\omega t + {\phi _1}} \right)$ and ${X_2} = a\sin \left( {\omega t + {\phi _2}} \right)$a resulting oscillation with the same time period and same amplitude is obtained. The value of ${\phi _1} - {\phi _2}$ is

Two sound waves with wavelength 5m and 6m respectively, each propagate in the gas with velocity 330 m/s. We except the following number of beats per second

A transverse wave of amplitude $0.5\,\,m$ and wavelength $1m$ and frequency $2\,\,Hz$ is propagating in a string in the negative $x$-direction. The expression for this wave is

Water waves are

The minimum audible wavelength at room temperature is about

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

Two waves having sinusoidal waveforms have different wavelengths and different amplitude. They will be having