Speed of a Travelling Wave

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is $n$. The internal energy of one mole of the gas is $U_n$ and the speed of sound in the gas is $v_n$. At a fixed temperature and pressure, which of the following is the correct option?

Which one among the following is true for the speed of sound in a given medium ?

Relation of wavelengths of sound and light is:

Equation of progressive wave is $y=A\sin \left(160t-0.5x\right)$. Let the speed of the wave be $10x$, then find $x$.

The equation of progressive wave is $y=5\sin \left(6t+0.03x\right)$. Find the speed of wave(in $\mathrm{m} {\mathrm{s}}^{-1}$).

A heavy rope is suspended from a rigid support. A wave pulse is set up at the lower end; then:

In a pond, ripples are sent, and a floating object goes up and down six times in $15 \mathrm{s}$. The wave crests are $0.4 \mathrm{m}$ apart. Calculate the wavelength, frequency and speed of water waves.

The equation of the standing wave is $y=0.02 \cos \left(\frac{2\mathrm{\pi }x}{60}\right)\sin \left(150\mathrm{\pi }t\right)$. Then the maximum velocity of the particle at a distance $10 \mathrm{m}$ is,

A sound wave has frequency of $2 \mathrm{kHz}$ and wavelength of $35 \mathrm{cm}$. If an observer is $1.4 \mathrm{km}$ away from the source, after what time interval could the observer hear the sound?

The distance between two successive minima of a transverse wave is $2.7 \mathrm{m}$. Five crests of the wave pass a given point along the direction of travel every $15.0 \mathrm{s}$. The speed of the wave is

Two strings $A$ and $B$ of same material of length $l$ and $\frac{l}{2}$, are subjected to tension $T$ and $2T$, respectively. The ratio of fundamental frequency of $A$ to fundamental frequency of $B$ is

Two pulses A and B have instantaneous velocities as shown by arrows. In which direction do these pulses travel in time?

One end of a horizontal string is attached to a vibrator which is vibrating at $60 \mathrm{Hz}$. The mass per unit length of the string is $3\mathrm{gm} {\mathrm{m}}^{-1}$. What should be the value of mass $m$ approximately so that the string vibrates in $5$ loops? Assume that the end of the string connected to the vibrator is a node.

A sound wave of frequency $440\mathrm{Hz}$ is passing through air. An ${\mathrm{O}}_2$ molecule (mass $=5.3\times {10}^{-26} \mathrm{kg}$) is set in oscillation with an amplitude of ${10}^{-6} \mathrm{m}$ speed at the centre of its oscillation is

A string of length $L$ is clamped between two points and speed of transverse wave in it is $500 \mathrm{m} {\mathrm{s}}^{-1}$. Now the tension is increased to four times just by making the string more tight. Neglect variation in length while increasing the tension. The new speed of transverse wave is

Fill in the blanks.
Wave velocity $=$ _____ $\times$ _____.

The drawing shows a frictionless incline and pulley. The two blocks are connected by a wire (mass per unit length, $\mu =25 \mathrm{g}/\mathrm{m}$) as shown in figure. A transverse wave on the wire has a speed of $60 \mathrm{m} {\mathrm{s}}^{-1}$ relative to it. Neglect the weight of the wire relative to the tension in the wire. If the mass ${\mathrm{m}}_2$ be increased by $1\%$, the speed of the transverse wave will be (in $\mathrm{m} {\mathrm{s}}^{-1}$): (Assume equilibrium initially)

Complete the following table:

Two ships are anchored a distance $d=3 \mathrm{km}$ apart in a sea, where seabed between the ships is at a uniform depth $h=1.0 \mathrm{km}$ and consists of a flat rock. Speed of sound in the air is $v_a=333 \mathrm{m} {\mathrm{s}}^{-1}$, in the water is $v_w=1.5 \mathrm{km} {\mathrm{s}}^{-1}$ and in the rock is $v_r=4.5 \mathrm{km} {\mathrm{s}}^{-1}$. If a gun is fired at a ship, the minimum time the firing will be heard at the other ship is $0.96x$ sec. Find the value of $x$ to the nearest integer.

The average density of Earth's crust $10 \mathrm{km}$ beneath the surface is $2.7 \mathrm{gm} {\mathrm{cm}}^{-3}$. The speed of longitudinal seismic waves at that depth is $5.4 \mathrm{km} {\mathrm{s}}^{-1}$. The bulk modulus of Earth's crust considering its behaviour as fluid at the depth is approximately a $\times {10}^b$. Find $b-a$. (Where a is rounded off to nearest single digit).