Question

$A$ is singing a note and at the same time $B$ is also singing a note with $1/8th$ the frequency of $A$. The energies of the two sounds are equal. The disparagement amplitude of the note if $B$ is:

• A. same as that of $A$
• B. Twice that of $A$
• C. four times that of $A$
• D. eigth times that of $A$

Answer 1

The correct option is D eigth times that of $A$

It is given that energy remains the same

Hence, $E_A=E_B$

$Energy\propto a^2{n}^2⟹\frac{a_B}{a_A}=\frac{n_A}{n_B}$ (Energy is same)

Therefore,

$(\frac{a_A}{a_B}{)}^2=(\frac{n_B}{n_A}{)}^2$

Given,

$n_A=n$

$n_B=\frac{n}{8}$

Therefore,

$\frac{n_A}{n_B}=\frac{n/8}{n}=\frac{1}{8}$

$⟹a_B=8a_A=8a$