Question

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 $P$.

• A. 40 cm/s
• B. 20 cm/s
• C. 2 mm/s
• D. 20 mm/s

Answer 1

Answer: (B)

Instantaneous power is given by
$P=\frac{F A^{2} \omega^{2}}{v} \cos ^{2}(\omega t-k x)$
We know that $v_{P}= A \omega \cos (\omega t-k x)$
$\Rightarrow P=\frac{F}{v} v_{P}^{2}$
$\Rightarrow 40 \times 10^{-3}=\frac{20}{20} v_{P}^{2}$
$\Rightarrow v_{P}=0.2\, m / s =20\, cm / s$