Question

Two sources of sound placed closed to each other, are emitting progressive waves given by y₁ = 4 sin 600 πt and y₂ = 5 sin 608πt. An observer located near these two sources of sound will hear:

(a) 4 beats/second with intensity ratio 25 : 16 between waxing and waning

(b) 8 beats/second with intensity ratio 25 : 16 between waxing and waning

(c) 8 beate/second with intensity ratio 81 : 1 between waxing and waning

(d) 4 beate/second witji intensity ratio 81:1 between waxing and waning

Answer 1

Correct option is : 4 beate/second witji intensity ratio 81:1 between waxing and waning

y₁ = 4 sin 600πt

y₂ = 5 sin 608πt

Comparing with the general equation

y = a sin 2πft

We get, f₁ = 300 Hz, f₂ = 304 Hz

So, number of beats = f₂ - f₁ = 4 s^-1

We know that,

\(\frac{I_{max}}{I_{min}} = (\frac{a_1 + a_2}{a_1 - a_2})^2\)

\((\frac{4 + 5}{4 - 5})^2 =81\)