Question-43 Two sources of sound are emitting progressive waves y_1=4\sin(710\pi t) and y_2=3\sin(702\pi t). The sources are placed close to each other. The number of beats heard per second and intensity ratio between waxing and waning are respectively
(A) 4,\ 16:9
(B) 8,\ 16:9
(C) 4,\ 49:1
(D) 8,\ 49:1
Answer : (C)
Explanation:
y₁ = 4 sin 710πt, y₂ = 3 sin 702πt
∴ ω₁ = 710π
2πf = 710π
f₁ = 355 Hz
A₁ = 4
and ω₂ = 702π
2πf = 702π
f₂ = 351 Hz
A₂ = 3
∴ Number of beats heard per second = f₁ − f₂ = 355 − 351 = 4
\frac{I_{max}}{I_{min}} = \frac{(A_1 + A_2)^2}{(A_1 - A_2)^2} = \frac{7^2}{1^2} = \frac{49}{1}