Two simple harmonic sound waves travelling in the same direction are given by $y_{1} (x, t) = A sin (0.5 π x - 100 π t)$ and $y_{2} (x, t) = A sin (0.46 π x - 92 π t)$
The number of times, a stationary listener can hear sound of maximum intensity in one second is

Question

TestHub · Accepted Answer

Comparing the given wave equations with the standard wave equation $y = A sin (k x - ω t)$ , we get the angular frequencies of the two waves as:

$ω_{1} = 100 π$

$ω_{2} = 92 π$

The frequencies of the two waves are:

$f_{1} = \frac{ω _{1}}{2 π} = \frac{100 π}{2 π} = 50$ Hz

$f_{2} = \frac{ω _{2}}{2 π} = \frac{92 π}{2 π} = 46$ Hz

The number of times a stationary listener hears sound of maximum intensity in one second is equal to the beat frequency.

Beat frequency $= ∣ f_{1} - f_{2} ∣$

Beat frequency $= ∣50 - 46∣ = 4$ Hz

Thus, the listener hears sound of maximum intensity $4$ times in one second.

Answer: $4$

Physics - Sound Wave Question with Solution | TestHub

Options:

Doubts & Discussion