Speed of a Travelling Wave

The equation of a wave on a string of linear mass density $0.04 \mathrm{kg} {\mathrm{m}}^{-1}$ is given by,  $y=0.02\left(\mathrm{m}\right)\sin \left[2\mathrm{\pi }\left(\frac{t}{0.04\left(\mathrm{s}\right)}-\frac{x}{0.50\left(\mathrm{m}\right)}\right)\right]$.

The tension in the string is $n\times {10}^{-2 }\mathrm{N}$. Write the value of $n$.

Speed of a transverse wave in a string depends on the tension and linear mass density of the string. Find the formula for the speed of the wave in the string.

Speed of a longitudinal wave in a medium is given by, $v=\sqrt{Ed}$, where E is elasticity of the medium and d is its density. 

Compare the velocities of the waveforms given below, and choose the correct option.

To increase the frequency from $100 \mathrm{Hz}$ to $400 \mathrm{Hz}$, the tension in the string has to be changed by,

The rope shown at an instant is carrying a wave travelling towards right, created by a source vibrating at a frequency $n$.

Consider the following statements:

Two Cu wires of radii $R_1$ and $R_2\text{,}$ such that $\left(R_1>R_2\right).$ Then, which of the following is true? 

A sonometer wire $1$ metre along weighing $2 \mathrm{g}$ is in resonance with a tuning fork of frequency $300 \mathrm{Hz}$. Magnitude of tension in Newton in the sonometer wire is 

A solid ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at the speed $60 \mathrm{cm} {\mathrm{s}}^{-1}$ on the string when the car is at rest. When the car accelerates on a horizontal road, speed of the pulse is $66 \mathrm{cm} {\mathrm{s}}^{-1}$. The acceleration of the car is nearly $\left(g=10 {\mathrm{ms}}^{-2}\right)$

A uniform rope of length $12 \mathrm{m}$ and mass $6 \mathrm{kg}$ hangs vertically from a rigid support. A block of mass $2 \mathrm{kg}$ is attached to the free end of the rope. A transverse pulse of wavelength $0.06 \mathrm{m}$ is produced at the lower end of the rope. Wavelength of the pulse when it reaches the top of the rope is ______.

The frequency of tuning fork is $500 \mathrm{Hz}$ and the velocity of sound in air is $300 \mathrm{m} {\mathrm{s}}^{-1}$. The distance travelled by sound while the fork executes $100$oscillations per second is ______.

The ratio of the speed of sound in nitrogen gas to that in helium gas at $300 \mathrm{K}$ is

What is the ratio of velocities of sound waves in oxygen and hydrogen if their density are in ratio $16:1$?

What will be the speed of the transverse wave in a $2.5 \mathrm{m}$ long rope hanging from the ceiling at the upper end and at a point $0.5 \mathrm{m}$ distance from the lower end respectively? Given the mass of the rope is $0.1 \mathrm{Kg}$ distributed uniformly.

Two steel wires $A$and $B$ are such that the diameter of $A$ is twice that of $B$ and the tension in $A$ is half of that in $B$. If transverse waves of same frequency are generated in both the wires, then compute the ratio of velocities of waves in $A$ and $B$.

A wave given by the equation $y = 0.021 \sin (x + 30t)$, where, $x$and $y$ are measured in metre and $t$in $\mathrm{second}$ is propagating in a string with linear density $1.3\times {10}^{-4} \mathrm{Kg} {\mathrm{m}}^{-1}$.  Calculate the tension in the string.

Considering the compositions of air to be $76\%$ Nitrogen and $26\%$ Oxygen by weight, calculate the velocity of sound in air. (Molecular weights of Nitrogen and Oxygen are $28$ and $32$, respectively, and $\gamma =1.4$.)

The respective displacements (in $\mathrm{cm}$) of two particles of a medium, disturbed by the wave propagation at $x_1=0 \mathrm{and} x_2=1 \mathrm{cm}$ can be given by the equations,

$y_1=2\sin 3\mathrm{\pi }t$
$y_{\mathrm{2}}=2\sin \left(3\mathrm{\pi }t\mathrm{-}\frac{\mathrm{\pi }}{8}\right)$

What is the wave speed?

Find the wave velocity for $20\le x\le \infty$.

A man standing between two parallel hills, claps his hand and hears successive echoes at regular intervals of $1 \mathrm{s}$. If velocity of sound is $340 \mathrm{m}\mathrm{ }{\mathrm{s}}^{-1}$, then the distance between the hills is