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

Options

A. same that of A
B. twice as that of A
C. four times as that of A
D. eight times as that of A

Answer

D

Explanation

It is given that energy remains the same
Hence `E_A=E_B`
energy `propa^2n^2implies(a_B)/(a_A)=(n_A)/(n_B)" "( ":.energy same ")`
`:. ((a_A)/(a_B))^2=((n_B)/(n_A))^2`
Given, `n_A=n,n_B=(n)/(8)`
`:. (a_A)/(a_B)=(n//8)/(n)=(1) rArr a_(B)=8a_(A)=8a`.