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The equation of a wave disturbance is given as : $y = 0.02 cos \left( {\frac{\pi }{2} + 50\pi t} \right) cos (10 x),$ where $x$ and $y$ are in meters and $t$ in seconds. Choose the wrong statement:
A metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T$ ($Y$ = young’s modulus, $\rho$ = density, $\alpha$ = coefficient of linear expansion) then the frequency of transverse vibration is proportional to :
Two sound waves with wavelengths $5.0\,\, m$ and $5 .5\,\, m$ respectively, each propagate in a gas with velocity $330\,\, m/s.$ We expect the following number of beats per second.
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
When a tuning fork of frequency $341$ is sounded with another tuning fork, six beats per second are heard. When the second tuning fork is loaded with wax and sounded with the first tuning fork, the number of beats is two per second. The natural frequency of the second tuning fork is