The maximum particle velocity in a wave motion is half the wave velocity. Then the amplitude of the wave is equal to

Question

Accepted Answer

Correct answer: A. (a) For a wave, y= asin ⁡( 2 πvt - 2 πx ) Here v= velocity of wave ∴y= asin ⁡( 2 πv t- 2 πx ) ∴ dy dt=a ( 2 πv ) cos ⁡( 2 πvt - 2 πx ) ∴ velocity = 2 πav cos ⁡( 2 πvt - 2 πx ) ∴ Maximum velocity is obtained when cos ⁡( 2 πvt - 2 πx )=1 ∴v_m= 2 πav ∴v_m= v2 (given) ∴ 2 πav = v2 or a= 4

$The maximum particle velocity in a wave motion is half the wave velocity. Then the amplitude of the wave is equal to$

Solution

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