A is singing a note and at the same time B is | vedclass

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(D) The energy $E$ of a sound wave is given by the relation $E \propto a^2 n^2$,where $a$ is the amplitude and $n$ is the frequency.Since the energies

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Eight times as that of $A$

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(D) The energy $E$ of a sound wave is given by the relation $E \propto a^2 n^2$,where $a$ is the amplitude and $n$ is the frequency.Since the energies of the two sounds are equal,we have $E_A = E_B$.Therefore,$a_A^2 n_A^2 = a_B^2 n_B^2$.Given that the frequency of $B$ is one-eighth the frequency of $A$,we have $n_B = \frac{1}{8} n_A$,or $\frac{n_A}{n_B} = 8$.Rearranging the energy equation: $\frac{a_B^2}{a_A^2} = \frac{n_A^2}{n_B^2}$.Taking the square root on both sides: $\frac{a_B}{a_A} = \frac{n_A}{n_B} = 8$.Thus,$a_B = 8 a_A$.The amplitude of the note of $B$ is eight times that of $A$.

$A$ is singing a note and at the same time $B$ is singing a note with exactly one-eighth the frequency of the note of $A$. If the energies of the two sounds are equal,the amplitude of the note of $B$ is:

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