Assertion (A): The average power transmitted by a progressive wave on a string is proportional to the square of the wave amplitude and the square of the angular frequency. Reason (R): The energy of a

Question

Assertion (A): The average power transmitted by a progressive wave on a string is proportional to the square of the wave amplitude and the square of the angular frequency.

Reason (R): The energy of a particle executing simple harmonic motion is proportional to the square of its amplitude and the square of its angular frequency. A. Both A and R are true and R is the correct explanation of A. B. Both A and R are true but R is not the correct explanation of A. C. A is true but R is false. D. A is false but R is true.

TestHub · Accepted Answer

The average power transmitted by a progressive wave on a string is given by $P_{a vg} = \frac{1}{2} μ A^{2} ω^{2} v$ , where $μ$ is linear mass density, $A$ is amplitude, $ω$ is angular frequency, and $v$ is wave speed. Thus, $P_{a vg} \propto A^{2} ω^{2}$ .

The energy of a particle executing simple harmonic motion (SHM) is $E = \frac{1}{2} m ω^{2} A^{2}$ . This shows that $E \propto A^{2} ω^{2}$ . A progressive wave transmits energy through the SHM of the medium particles.

Therefore, the power transmitted by the wave is directly related to the energy of the oscillating particles, and the proportionality stated in R explains the proportionality in A.

Physics - Wave on String Question with Solution | TestHub

Options:

Doubts & Discussion