Question

Two sources of sound placed close to each other, are emitting progressive waves given by $y _{1}=4 \sin 600\, \pi t$ and $y _{2}=5 \sin 608\, \pi t :$ An observer located near these two sources of sound will hear

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

Answer 1

Answer: (D)

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

Answer 2

The correct answer is D:4 beats per second with intensity ratio $81\ratio 1$ between waxing and waning
Comparing with $y _{1}= a _{1} \sin 2 \pi f _{1} t$
and $y _{2}= a _{2} \sin 2 \pi f _{2} t$
we get $f_1 =300\, Hz,\, f _{2}=304\, Hz$
Number of beats $= f _{2}- f _{1}=4\, s ^{-1}$
$\frac{ I _{\max }}{ I _{\min }}=\left(\frac{ a _{1}+ a _{2}}{ a _{1}- a _{2}}\right)^{2}$
$=\frac{ I _{\max }}{ I _{\min }}=\left(\frac{4+5}{4-5}\right)^{2}=\frac{81}{1}$