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Two sources of sound placed close to each other, are emitting progressive waves given by $y_1 = 4\sin600\pi t$ and $y_2 = 5\sin608\pi t$. An observer located near these two sources of sound will hear:
A
4 beats per second with intensity ratio 81 : 1 between waxing and waning
B
4 beats per second with intensity ratio 25 : 16 between waxing and waning
C
8 beats per second with intensity ratio 25 : 16 between waxing and waning
D
8 beats per second with intensity ratio 81 : 1 between waxing and waning
Detailed Solution
$\omega_1 = 600\pi \Rightarrow f_1 = 300$ Hz; $\omega_2 = 608\pi \Rightarrow f_2 = 304$ Hz
Beat frequency $= 304 - 300 = 4$ beats per second
$\frac{I_{max}}{I_{min}} = \frac{(A_1 + A_2)^2}{(A_1 - A_2)^2} = \frac{(4 + 5)^2}{(5 - 4)^2} = \frac{81}{1}$
So the observer hears 4 beats per second with intensity ratio 81 : 1.
Beat frequency $= 304 - 300 = 4$ beats per second
$\frac{I_{max}}{I_{min}} = \frac{(A_1 + A_2)^2}{(A_1 - A_2)^2} = \frac{(4 + 5)^2}{(5 - 4)^2} = \frac{81}{1}$
So the observer hears 4 beats per second with intensity ratio 81 : 1.