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A simple harmonic progressive wave is gi...

A simple harmonic progressive wave is given by the equation, ` y = 0.1 sin 4 pi (50 t - 0.2 x)` in SI units. Find the period, wavelength and speed of the wave.

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Data : ` y = 0.1 sin 4 pi (50 t - 0.2 x) = 0.1 sin 2 pi (100 t -0.4 x)`
`= 0.1 sin 2pi (100 t - x/2.5) ` (in SI units )
Equating the above equation to that of a simple harmonic progressive wave.
` y = A sin 2 pi ( nt - x/lamda) = 0.1 sin 2pi (100t - x/2.5) ` we get
n = 100 Hz, and ` lamda = 2.5 m`
(i) the period ` (T) = 1/n = 1/100 =0.01 s`
(ii) The wavelength `(lamda) = 2.5 m` (iii) The speed of the wave (v) = `n lamda = 100 xx 2.5 = 250 ` m/s
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