Question

The equation of progressive wave travelling along positive x-axis is
$y = 0.3 \sin10\pi(2x - 3t)$
where 'x','y' are in metre and 't' in second.Find:
i) Amplitude
ii) Wave length
iii) Period
iv) Frequency
v) Wave velocity​

Answer 1

Explanation:

FINAL EQUATION WILL BE $y=0.3sin(20\pi x-30\pi t)$

Comparing with standard equation Asin(kx-ωt)

1] AMPILTUDE = 0.3

2] WAVE LENGTH - k = 20π   ⇒2π/λ = 20π    ⇒ λ = 2/20 = 0.1

3] FREQUENCY - ω=30π ⇒ 2πf = 30π ⇒ f= 1/15 hz

4] Wave velocity = ω*λ =  1/15*2/20  =   1/150

5] Period T = 1/f = 15s.

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