Equation of a progressive wave is given by $y = a\,\sin \pi \,\left[ {\frac{t}{2} - \frac{x}{4}} \right]\,,$ where $t$ is in seconds and $x$ is in meters. The distance through which the wave moves in $8 sec$ is .... $(m)$ (in meter)
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A train moves towards a stationary observer with speed $34 m/s$. The train sounds a whistle and its frequency registered by the observer is ${f_1}$. If the train’s speed is reduced to $17\, m/s$, the frequency registered is ${f_2}$. If the speed of sound is 340 m/s then the ratio ${f_1}/{f_2}$ is
An observer is approaching with a speed $v$, towards a stationary source emitting sound waves of wavelength $\lambda_0$. The wavelength shift detected by the observer is (Take $c=$ speed of sound)
The path difference between the two waves ${y_1} = {a_1}\sin \,\left( {\omega t - \frac{{2\pi x}}{\lambda }} \right)$ and ${y_2} = {a_2}\cos \,\left( {\omega t - \frac{{2\pi x}}{\lambda } + \phi } \right)$ is
In the figure shown a mass $1\ kg$ is connected to a string of mass per unit length $1.2\ gm/m$ . Length of string is $1\ m$ and its other end is connected to the top of a ceiling which is accelerating up with an acceleration $2\ m/s^2$ . A transverse pulse is produced at the lowest point of string. Time taken by pulse to reach the top of string is .... $s$