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. The energies of two sounds are equal, the amplitude of the note of B is
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It is given that energy remains the same
Hence $E_{A} = E_{B}$
$energy \propto a^{2} n^{2} \Rightarrow \frac{a_{\mathrm{B}}}{a_{\mathrm{A}}} = \frac{n_{\mathrm{A}}}{n_{\mathrm{B}}} \quad (: \text{energy same}) \\ \therefore \left(\frac{a_{\mathrm{A}}}{a_{\mathrm{B}}}\right)^{2} = \left(\frac{n_{\mathrm{B}}}{n_{\mathrm{A}}}\right)^{2}$
Given, $n_A = n, n_B = \frac{n}{8}$
$\therefore \frac{a_A}{a_B} = \frac{n/8}{n} = (1) \Rightarrow a_B = 8a_A = 8a.$
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