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Q.

A transverse wave is passing through a stretched string with a speed of 20 m/s. The tension in the string is 20 N. At a certain point P on the string, it is observed that energy is being transferred at a rate of 40 mW at a given instant. Find the speed of point P.

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a

40 cm/s

b

20 cm/s

c

2 mm/s

d

20 mm/s

answer is B.

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Detailed Solution

Instantaneous power is given byP = FA2ω2vcos2(ωt-kx)We know that vp = Aωcos(ωt-kx)⇒P =Fvvp2⇒40×10-3 = 2020vp2 ⇒ vp = 0.2 m/s = 20 cm/s

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