Question

The equation of longitudinal stationary wave is y=6sin 2pi/6xcos160pi*t where x and y are in cm and t is in sec . find i) frequency ii) amplitude iii)wavelength iv) separation between two successive nodes v) equation of progressive waves.

Answer 1

Dear student,
$$\begin{gathered} Compairingtheequationy=6\sin \frac{2\pi x}{6}\cos 160\pi twith \\ y=A\sin kx\cos \omega t \\ Sok=\frac{2\pi }{6}=\frac{\pi }{3} \\ \omega =160\pi \\ A=amplitude=6cm \\ \omega =2\pi f, \\ sof\left(frequency\right)=\frac{2\pi }{\omega }=\frac{2\pi }{160\pi }=\frac{1}{80}Hz \\ wavelength\lambda =\frac{2\pi }{k}=\frac{2\pi }{\frac{\pi }{3}}=6cm \\ separationbetweentwosuccessivenodes=\frac{\lambda }{2}=\frac{6}{2}=3cm \end{gathered}$$

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