Displacement Relation for a Progressive Wave

The wave function of a pulse is given by $y=\frac{5}{1+{\left(4x+6t\right)}^2}$ where$x$and $y$ are in metre and$t$is in second. The velocity of pulse is 

The same progressive wave is represented by two graphs$I$and$II$. Graph $I$shows how the displacement $y$ varies with the distance$x$along the wave at a given time. Graph II shows how y varies with time tat a given point on the wave. The ratio of measurements$AB$ to $CD$, marked on the curves

Snapshot of a wave travelling in positive$x-$direction is taken, as shown in figure, at an instant. Which of the following represent the correct combination of the points as time passes at the instant shown.

The equation of wave is given by $Y={10}^{-2}\sin 2\pi \left(160t-0.5x+\frac{\pi }{4}\right)$, where $x$ and $Y$ are in $m$ and $t$ in $s$. The speed of the wave is _______ $\mathrm{km} {\mathrm{h}}^{-1}$.

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

The figure shows the position-time graph of an object in SHM. The correct equation representing this motion is

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The diagram below shows past of a travelling wave travelling along a string having linear mass density $10 \mathrm{g} {\mathrm{cm}}^{-1}$. Find the average power transmitted by the wave if wave propagates at frequency $10 \mathrm{Hz}$. (in Watt) Take ${\pi }^2=10$

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 $\mathrm{m} {\mathrm{s}}^{-1}$).

The coordinates of a moving particle at a time$t$ are given by $x=5\sin 10t$, $y=5\cos 10t$. The speed of the particle is:

A particle oscillates in SHM according to the equation $x=10\cos (2\pi t+\frac{\pi }{4})$, its acceleration at $t$ equal to $1.5$ seconds is

A simple harmonic wave of amplitude$8$unit travels along the positive x-axis. At given instant of time, for a particle at a distance of $10 \mathrm{cm}$ from the origin, the displacement is $+6$ unit and for a particle at a distance of $25 \mathrm{cm}$ from the origin, the displacement is $+4$unit. Calculate the wavelength(in $\mathrm{cm}$).

Loudness of sound coming from a point source at a distance $R$ is $50\mathrm{dB}$. If the distance is doubled then the new loudness value will become approximately.

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

Which of the following equations does not represent a progressive wave?

The wave function of a triangular wave pulse is defined by the relation below at time $t=0$ sec.

$y=\left\{\begin{array}{c}\begin{array}{l} \\ mx\end{array}\\ -m\left(x-a\right)\\ 0\end{array}\right.\begin{array}{c}\begin{array}{l}\mathrm{for} 0\le x\le \frac{a}{2}\\ \begin{array}{c}\mathrm{for} \frac{a}{2}\le x\le a\\ \mathrm{every} \mathrm{where} \mathrm{else}\end{array}\end{array}\end{array}$

The wave pulse is moving in the $+x$ direction in a string having tension $T$ and mass per unit length $\mu$. The total kinetic energy present with the wave pule 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

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.