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.

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

Tardigrade Admin · Accepted Answer

Instantaneous power is given by P=(F A2 ω2/v) cos 2(ω t-k x) We know that vP= A ω cos (ω t-k x) ⇒ P=(F/v) vP2 ⇒ 40 × 10-3=(20/20) vP2 ⇒ vP=0.2 m / s =20 cm / s

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 $P$ .

40 cm/s

20 cm/s

2 mm/s

20 mm/s

Instantaneous power is given by
$P = \frac{F A ^{2} ω ^{2}}{v} cos^{2} (ω t - k x)$
We know that $v_{P} = A ω cos (ω t - k x)$
$\Rightarrow P = \frac{F}{v} v_{P}^{2}$
$\Rightarrow 40 \times 1 0^{- 3} = \frac{20}{20} v_{P}^{2}$
$\Rightarrow v_{P} = 0.2 m / s = 20 c m / s$

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