Question

The average power transmitted through a given point on a string supporting a sine wave is $0.40watt$ when the amplitude of wave is $2mm$. What average power will transmitted through this point its amplitudes is increased to $4mm$?

• A. $0.40watt$
• B. $0.80watt$
• C. $1.2watt$
• D. $1.6watt$

Answer 1

The correct option is D $1.6watt$

The energy of a particle performing SHM is given by $E=\frac{1}{2}k{A}^2$

Whenever there is a sine wave passing through any medium, the particles are performing SHM. Hence their energy is the same as the equation above.

We know that power $P=\frac{energy}{time}$

$\therefore P=\frac{1}{2t}k{A}^2$

In the given problem, A is doubled, so power will increase 4 times.

Hence Correct answer is 1.6watt.