If a wave propagates through a medium, then the velocity of particle of medium is given by :
The wave equation is given by:
$$y=A sin (\omega t-kx)$$
Particle velocity= $$v_p=\dfrac{\partial y}{\partial t}=A\omega cos(\omega t-kx)$$ ...(1)
Strain= $$\dfrac{\partial y}{\partial x}=-Akcos(\omega t-kx)$$ ...(2)
Dividing the two equations we get,
$$\dfrac{v_p}{strain}=\dfrac{\omega}{k}$$ {taking the mod value of K]
Now $$\dfrac{\omega}{k}=\dfrac{2\pi}{T}\times \dfrac{\lambda}{2\pi}=\dfrac{\lambda}{T}= \text{wave velocity}$$
$$\therefore v_p=\text{wave velocity}\times strain$$
The equation of a travelling sound wave is $$y = 6.0 \sin (600 t - 1.8 x)$$ where y is measured in $$10^{-5}m$$ in second and $$x$$ in meter. (a) Find the ratio of the displacement amplitude of the particles to the wavelength of the wave. (b) Find the ratio of the velocity amplitude of the particles to the wave speed.
A sinusoidal transverse wave of amplitude $$ y_{m} $$ and wavelength $$ \lambda $$ travels on a stretched cord. Find the ratio of the maximum particle speed (the speed with which a single particle in the cord moves transverse to the wave) to the wave speed.
The amplitude of a wave disturbance propagating in the positive $$x-$$-direction is given by: $$y=\dfrac{1}{1+x^2}$$ at $$t=0$$ and $$y=\dfrac{1}{[1+(x-1)^2]}$$ at $$t=2$$ sec. Where, $$x$$ and $$y$$ are in meters. If the shape of the wave disturbance does not change during the propagation, what is the velocity of the wave?
The diagram shows an instantaneous position of a string as a transverse progressive wave travels along it from left to right. Which one of the following correctly shows the direction of the velocity of the points $$1,\, 2$$ and $$3$$ on the string?
The equation of a travelling wave is given by $$y=0.1\sin \left(\dfrac{5}{11}\pi x-10\pi t\right)$$ where $$y$$ and $$x$$ are in $$cm$$ and $$t$$ in second. The maximum speed of a particle of the medium due to wave is:
A transverse wave is described by the equation $$y= y_{0}sin 2\pi \left ( ft-\frac{x}{\lambda } \right )$$ The maximum particle velocity is equal to four time the wave velocity if
Mark the correct statement:
The equation of a progressive wave travelling along a string is given by $$y = 10 \,sin\pi \,(0.01x - 2.00t)$$ where x and y are in centimetres and t in seconds. Find the (i) velocity of a particle at $$x = 2 \,m$$ and $$t = \dfrac{5}{6 }\,s.$$ (ii) acceleration of a particle at $$x = 1 \,m$$ and $$t = \dfrac{1}{4} \,s.$$ Also find the velocity amplitude and acceleration amplitude for the wave.
A travelling wave pulse is given by $$y = \dfrac {0.8}{(3x^2 + 12xt + 12 t^2 + 4)}$$ where x and y are in m and t is in s. Find the velocity and amplitude of the wave.
The equation of a wave travelling on a string is $$y = 4\,sin \dfrac {\pi}{2}\left ( 8t - \dfrac {x}{8} \right )$$ if x and y are in centimetres, then velocity of wave is