A long taut string is connected to a harmonic oscillator of frequency ' f ' at one end. The oscillator oscillates with an amplitude ' a 0 ' and delivers power ' p 0 '

Question

A long taut string is connected to a harmonic oscillator of frequency ' f ' at one end. The oscillator oscillates with an amplitude ' $a_{0}$ ' and delivers power ' $p_{0}$ ' to the string. Due to dissipation of energy the amplitude of wave goes on decreasing with distance 'x' from the oscillator given as $a = a_{0} e^{- kx}$ where k is constant. Upto what distance from the oscillator, the power dissipated is equal to 3/4 th of power supplied by the source?

Options:

Answer:

B

Solution:

$P = \frac{p _{0}}{4} p α a^{2}, a^{- 2 kx} = \frac{1}{4}, 2 kx = ℓ n 4, x = \frac{ℓ n 2}{k}$

TestHub · Accepted Answer

P = 4 p 0 ​ ​ p α a 2 , a − 2 kx = 4 1 ​ , 2 kx = ℓ n 4 , x = k ℓ n 2 ​

Physics - Wave on String Question with Solution | TestHub

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