Question

Two sound waves each of amplitude $a$ and of frequencies $500Hz$ and $512Hz$ superpose. Then the resultant of the amplitude of the resultant wave at $t=\frac{5}{48}s$ is

• A. $0$
  
• B. $\frac{a}{\sqrt{2}}$
• C. $a\sqrt{2}$
• D. $2a$

Answer 1

The correct option is B $\frac{a}{\sqrt{2}}$

When two sound waves of slightly different frequencies and equal amplitudes superimpose on each other, then their resultant amplitude is given by

$R=2a\cos \left(2\pi \frac{n_1-n_2}{2}t\right)=2a\cos (2\pi \times \frac{512-500}{2}\times \frac{5}{48})=\frac{a}{\sqrt{2}}$

Note that here the angle is in radians.

Substitute and calculate.