Question

Two sound waves having displacements $y_1 = 2sin(1000 \pi t)$ and $y_2 = 3sin(1006 \pi t)$ when interfere, produce

• A. 5 beats/s with maximum intensity 25 units
• B. 3 beats/s with maximum intensity 25 units

Answer 1

Answer: (B)

3 beats/s with maximum intensity 25 units

Answer 2

Wave frequencies are given by:

$f_1 = \frac{1000\pi}{2\pi} = 500\ \text{Hz}$ and $f_2 = \frac{1006\pi}{2\pi} = 503\ \text{Hz}$.

The beat frequency is:

$f_\text{beats} = |f_2 - f_1| = |503 - 500| = 3\ \text{Hz}$.

The maximum amplitude occurs when the waves are in phase:

$A_{\text{max}} = 2 + 3 = 5$,

and the corresponding maximum intensity (proportional to amplitude squared) is:

$I_{\text{max}} \propto 5^2 = 25$.