Two sound waves travelling in the same direction have displacement y 1 = a sin ( 0.2 π x − 50 π t ) and y 2 = a sin ( 0.15 π x − 46 π t ) How many times, a listener can hear sound of maximum i

Question

Two sound waves travelling in the same direction have displacement ​ y 1 ​ = a sin ( 0.2 π x − 50 π t ) and y 2 ​ = a sin ( 0.15 π x − 46 π t ) ​ How many times, a listener can hear sound of maximum intensity in one second?

TestHub · Accepted Answer

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

$ω_{1} = 50 π$

$ω_{2} = 46 π$

The frequencies of the two sound waves are:

$f_{1} = \frac{ω _{1}}{2 π} = \frac{50 π}{2 π} = 25$ Hz

$f_{2} = \frac{ω _{2}}{2 π} = \frac{46 π}{2 π} = 23$ Hz

The number of times a listener hears maximum intensity in one second is equal to the beat frequency, which is the difference between the two frequencies:

$n = f_{1} - f_{2}$

$n = 25 - 23 = 2$

Answer: 2

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