Question

The ratio of amplitude of two waves is 3:4. What is the ratio of their:
(i) loudness? (ii) frequencies?

Answer 1

(i) Loudness of sound is directly proportional to the square of amplitude i.e.,

Loudness $\left(L\right)\propto a^2$

Ratio of Loudness $=\frac{L_1}{L_2}=\frac{a_{1^2}}{a_{2^2}}=\frac{(3{)}^2}{(4{)}^2}=\frac{9}{16}=9:16$

(ii) Change in amplitude of a sound does not affect its frequency.

$\therefore$ Ratio of frequencies remains same $=1:1$