Question

Following two wave trains are approaching each other. y1 = a sin 200 π t y2 = a sin 208 π t The number of beats heard per second is :

Answer 1

Given, y₁ = asin200πt
y₂ = asin208πt

We know, standard from of wave is y = asin(2πf)t
Where f is the frequency of wave

∴frequency of wave y₁ = 200π/2π = 100 Hz
Frequency of wave y₂ = 208π/2π = 104Hz

∵ number of Beats heard per second = difference in frequency of two of same Amplitude
∴ number of Beats heard per second = frequency of wave y₂ - frequency of wave y₁
= 104 Hz - 100 Hz
= 4Hz

Hence , number of Beats heard per second = 4