Two sources of sound placed close to each other are wmitting progressive waves given by `y_1=4sin600pit` and `y_2=5sin608pit`. An observer located near these two sources of sound will hear:

Options

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

B

Explanation

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 f1=300 Hz, `f_(2)=304 Hz` Number of beats `=f_(2)-f_(1)=4s^(-1)`
`(I_("max"))/(I_("min"))=((a_(1)+a_(2))/(a_(1)-a_(2)))^(2)=(I_("max"))/(I_("min"))=((4+5)/(4-5))^(2)=(81)/(1)`