Wave equations of two particles are given by ${y_1} = a\sin (\omega \,t - kx)$, ${y_2} = a\sin (kx + \omega \,t)$, then
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(a) Both waves are moving opposite to each other .
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A train moves towards a stationary observer with a speed $34 \,m / s$. The train sounds a whistle and its frequency registered by the observer is $f_1$. If the speed of the train is reduced to $17 \,m / s$, the frequency registered is $f_2$. If the speed of sound is $340 \,m / s$ then the ratio $\frac{f_1}{f_2}$ is ..........
The average density of Earth’s crust $10\ km$ beneath the surface is $2.7\ gm/cm^3$ . The speed of longitudinal seismic waves at that depth is $5.4\ km/s$ . The bulk modulus of Earth’s crust considering its behaviour as fluid at that depth is
The vibrations of a string of length $60\, cm$ fixed at both the ends are represented by the equation $y = 2\,\sin \,\left( {\frac{{4\pi x}}{{15}}} \right)\,\cos \,\left( {96\pi t} \right)$ where $x$ and $y$ are in $cm$. The maximum number of loops that can be formed in it is
An observer receives waves directly from a source of sound distant $120\,m$ in a big hall. He also receives waves reflected from the mid-point of $25\,m$ high ceiling. The wavelength of sound for constructive interference to take place between two waves, must be :
A progressive wave travelling in positive $x$-direction given by $y=a \cos (k x-\omega t)$ meets a denser surface at $x=0, t=0$. The reflected wave is then given by
An open organ pipe of length $l$ is sounded together with another organ pipe of length $l + x$ in their fundamental tones $(x < < l)$. The beat frequency heard will be (speed of sound is $v$) :
Two points on a travelling wave having frequency $500\, Hz$ and velocity $300\, m/s$ are $60^o$ out of phase, then the minimum distance between the two points is ..... $m$
Two adjacent piano keys are struck simultaneously. The notes emitted by them have frequencies ${n_1}$ and ${n_2}$. The number of beats heard per second is