Question

When beats are produced by two progressive waves of same amplitude and of nearly the same frequency, then the maximum loudness heard, corresponding to each of the constituent waves is:

• A. two times
• B. eight times
• C. four times
• D. same

Answer 1

The correct option is C four times

We know that intensity $I\propto a^2$,

where a is the amplitude of the wave.

The maximum amplitude is the sum of two amplitudes i.e.,

$(a+a=2a)$.

Hence, maximum intensity

$\propto (2a{)}^2\to \propto 4a^2$.

Therefore, the required ratio i.e.,

the ratio of maximum intensity (loudness) and intensity (loudness) of one wave is given by n,

$n=\frac{4a^2}{a^2}=4$