Two sources of sound placed close to each other, are emitting progressive waves given by y_1=4 600 π t and y_2=5 608 π t An observer located near these two sources of sound will hear

Correct answer: D. 4 beats per second with intensity ratio 81: 1 between waxing and waning Given, y_1=4 600 π t and y_2=5 608 π t Comparing with general equation y=a 2 π f t we get, f_2=300 ~Hz and f_2=304 ~Hz Number of beats =f_2-f_1=4 ~s^ -1 aligned I_ I_ & =((a_1+a_2)/(a_1-a_2))^2 & =((4+5)/(4-5))^2=(81)/(1) aligned

NEET 2012

Exam: NEET
Year: 2012
Subject: Physics
Chapter: Waves and Sound

NEET 2012 · Physics · Waves and Sound

Two sources of sound placed close to each other, are emitting...

Two sources of sound placed close to each other, are emitting progressive waves given by

y_1=4 \sin 600 \pi t \text{ and } y_2=5 \sin 608 \pi t

An observer located near these two sources of sound will hear

Options

A4 beats per second with intensity ratio $25: 16$ between waxing and waning
B8 beats per second with intensity ratio $25: 16$ between waxing and waning
C8 beats per second with intensity ratio $81: 1$ between waxing and waning
D4 beats per second with intensity ratio $81: 1$ between waxing and waning

Correct answer

D. 4 beats per second with intensity ratio $81: 1$ between waxing and waning

Step-by-step solution

Given,

y_1=4 \sin 600 \pi t

and

y_2=5 \sin 608 \pi t

Comparing with general equation

y=a \sin 2 \pi f t

we get,

f_2=300 \mathrm{~Hz}

and

f_2=304 \mathrm{~Hz}

Number of beats

=f_2-f_1=4 \mathrm{~s}^{-1}

\begin{aligned} \frac{I_{\max }}{I_{\min }} & =\left(\frac{a_1+a_2}{a_1-a_2}\right)^2 \\ & =\left(\frac{4+5}{4-5}\right)^2=\frac{81}{1} \end{aligned}

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