A musical instrument X produces sound waves of frequency n and amplitude A . Another musical instrument Y produces sound waves of frequency 3 n . The waves produced by x and y have equal energies. T

Question

A musical instrument X produces sound waves of frequency n and amplitude A . Another musical instrument Y produces sound waves of frequency 3 n ​ . The waves produced by x and y have equal energies. The amplitude of waves produced by Y will be

TestHub · Accepted Answer

The energy of a sound wave is directly proportional to the square of its frequency and the square of its amplitude.

$E \propto n^{2} A^{2}$

For instrument X, the energy is $E_{X} \propto n^{2} A^{2}$ .

For instrument Y, the energy is $E_{Y} \propto (\frac{n}{3})^{2} A_{Y}^{2}$ .

Given that the waves produced by X and Y have equal energies, we have $E_{X} = E_{Y}$ .

$n^{2} A^{2} = (\frac{n}{3})^{2} A_{Y}^{2}$

$n^{2} A^{2} = \frac{n ^{2}}{9} A_{Y}^{2}$

$A_{Y}^{2} = 9 A^{2}$

$A_{Y} = 3 A$

Answer: 3 A

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