A steel wire has a mass of and is under tension . The maximum average power that can be carried by the transverse wave in the wire if the amplitude is not to exceed of the wavelength is ____ kW.

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Concept- The average power would be 1080kW. Solution of this problem can found out by average power formula,
So,

The time-averaged power of a sinusoidal wave on a string is found by average power

, Average power

, , where

is the linear mass density of the string,

is the amplitude of the wave,

is the wave's angular frequency, and V represents the wave's velocity.
Each wave's amplitude and frequency determine its power. If each wavelength's power is thought of as a separate packet of power, a high-frequency wave will produce more of such packets in a given amount of time than a low-frequency wave. We'll find that the common rate of power transfer in mechanical waves is proportional to both the frequency and each amplitude's square.
Using the average power formula to solve, we obtain

So, for calculating velocity we solve, Question Image

The Maximum Average Power is therefore determined as

Hence, the answer is 1080 kW.

Watch 3-min video & get full concept clarity