Question

Two source of sound placed closed to each other, are emitting progressive wave given by $y_1=4\sin 600\pi t$ and $y_2=5\sin 608\pi t$. An observed located near these two sources will hear:

• A. $8$ beats per second with intensity ratio $81:1$ between waxing and waning
• B. $4$ beats per second with intensity ratio $81:1$ between waxing and waning
• C. $4$ beats per second with intensity ratio $25:16$ between waxing and waning
• D. $8$ beats per second with intensity ratio $25:16$ between waxing and waning

Answer 1

The correct option is B $4$ beats per second with intensity ratio $81:1$ between waxing and waning

Given

$y_1=4\sin 600\pi t{y}_2=5\sin 608\pi t$

Comparing with general equation

$y=a\sin 2\pi ft$

we get,

$f_1=300f_2=304$

then,

Number of beats$=304-300=4beats/sec$

Intensity ratio is given as,

$\frac{I_{max}}{I_{min}}={\left(\frac{a_1+a_2}{a_1-a_2}\right)}^2$

$\frac{I_{max}}{I_{min}}={\left(\frac{4+5}{4-5}\right)}^2$

$\frac{I_{max}}{I_{min}}=\left(\frac{81}{1}\right)$

$\therefore I_{max}:I_{min}=81:1$