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

Answer

D

Explanation

Here, `y_(1)=4sin 600pit=a_(1)sin 2pin_(1)t`
`:. a_(1)=4,n_(1)=(600pi)/(2pi)=300Hz`
`y_(2)=5sin608pit=a_(2)sin 2pin_(2)t`
`,. a_(2)=5,n_(2)=(608pi)/(2pi)=240Hz`
Number of beats `//` sec `=n_(2)-n_(1)=304-300=4`
`(I_(max))/(I_(min))=((a_(1)+a_(2))^(2))/((a_(1)-a_(2))^(2))=((4+5)^(2))/((4-5)^(2))=(81)/(1)`