Velocity and Acceleration of Particles in Wave Motion

How can we determine the particle acceleration of a sinusoidal wave?

Acceleration of a particle at any time of a sinusoidal wave is constant.

A particle performing SHM is given by the equation

$y=A\sin \left(\omega t\right)$

Which one of the following is the correct formula for the maximum acceleration of this particle?

Two sound waves of frequencies $100 \mathrm{Hz}$ and $102 \mathrm{Hz}$ and having the same amplitude $A$ are interfering. A detector which can detect waves of amplitude greater than or equal to $A$ is kept at rest. In a time interval of $12$ seconds, find the total duration in which detector is active.

The diagram shows an instantaneous position of a string as a transverse progressive wave that travels along it from left to right. Which one of the following correctly shows the direction of the velocity of points $1, 2$ and $3$ on the string?

The figure shows the wave $y=A\sin \left(\mathrm{\omega }t-kx\right)$. What is the magnitude of the slope of the curve at $B ?$

The figure below shows the wave $y=A\sin (\omega t-kx)$ at any instant travelling in the $+\mathrm{ve} x$ -direction. What is the magnitude of the slope of the curve at $B$ :

A progressive wave is represented by

$y = 0.1 \sin \frac{8\pi }{7} \left(0.1t-\frac{x}{20}\right)$

Where all the observations are in MKS system. The wave velocity will be -

The transverse wave shown is travelling from right to left in a medium. The direction of the instantaneous velocity of a particle of the medium at point $P$ is

When a wave travels in a medium, displacement of a particle is given by $y=a\sin \left[2\pi (bt-cx)\right]$ where a, b, c are constants. The maximum particle velocity will be twice the wave velocity if

A mass and spring system oscillates with amplitude $\mathrm{A}$ and angular frequency $\mathrm{\omega }$ -

A transverse wave is described by the equation, $y=y_0\sin 2\mathrm{\pi }\left(ft-\frac{x}{\lambda }\right)$. The maximum particle velocity is equal to four times the wave velocity, if

A wave travelling in stretched string is described by the equation $y=\mathrm{A}\mathrm{s}\mathrm{i}\mathrm{n}(kx-\omega t)$.The maximum particle velocity is

A wave travelling along a string is described by the equation $y=a\sin \left(\omega t-kx\right)$ the maximum particle velocity is

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

A transverse sinusoidal wave moves along a string in positive $x$-direction at a speed of $10 \mathrm{c}\mathrm{m} {\mathrm{s}}^{-2}$. The wavelength of the wave is $0.5 \mathrm{m}$ and its amplitude is $10 \mathrm{cm}$ at a particular time $t$, the snap-shot of the wave is shown in figure. The velocity of point $P$ when its displacement is $5 \mathrm{cm}$ is

If the equation of transverse wave is $y=\sin (kx-2t)$, then the maximum particle velocity is

A wave pulse is generated in a string that lies along $x$-axis. At the points $\mathrm{A}$ and B, as shown in the figure, if $R_{\mathit{A}}$ and $R_{\mathrm{B}}$ are the ratio of wave speed to the particle speed respectively then :

When a sound wave of wavelength$\lambda$. is propagating in a medium, the 'maximum velocity' of the particle is equal to the wave velocity. The amplitude of wave is

A transverse sinusoidal wave moves along a string in the positive x-direction at a speed of 10 cm/s. The wavelength of the wave is 0.5 m and its amplitude is 10 cm. At a particular time t, the snap-shot of the wave is shown in figure. The velocity of point P when its displacement is 5 cm is