Question

Equation of a plane progressive simple harmonic wave is y = 0.02sin (20t - 1/25x + pie/6). The speed of wave is (all symbols have their usual meaning and all quantities are in S.I units)

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Answer 1

Equation of a plane progressive simple harmonic wave is y = 0.02sin (20t - 1/25x + pie/6).

we know, standard equation of plane progressive wave is given by, $y=Asin(\omega t-kx+\phi)$

comparing with standard equation of plane progressive wave,

so, A = 0.02m, $\omega$ = 20rad/s , k = 1/25 and $\phi=\frac{\pi}{6}$

we know, k = 2π/$\lambda$

so, 1/25 = 2π/$\lambda$

or, $\lambda$ = 50π m.....(1)

and $\omega=\frac{2\pi}{\eta}$

20 = 2π$\eta$

or, $\eta$ = 10/π cycle/sec ......(2)

speed of wave , v = $\lambda\eta$

$\lambda$ is wavelength while $\eta$ is frequency of wave.

so, speed of wave, v = 50π × 10/π

= 500 m/s