Question

A microphone is located on the line connecting two speakers that are 0.513 m apart and oscillating in phase. The microphone is 1.80 m from the midpoint of the two speakers. What are the lowest two frequencies that produce an interference maximum at the microphone's location?

Answer 1

frequency 1 = 334.30 Hz

frequency 2 = 1002.92 Hz

Step-by-step explanation:

Given data

speaker distance y = 0.513 m

microphone distance D = 1.80 m

to find out

lowest two frequencies

solution

we know velocity of sound is 343 m/s

so we consider point x

so at 1st speaker distance from x = D + (y/2)

1st speaker distance from x = 1.80 + (0.513/2) = 2.0565 m .....1

and

at 2nd speaker distance from x = D - (y/2)

2nd speaker distance from x = 1.80 - (0.513/2) = 1.5435 m .........2

so destructive interference from 1 and 2 we know

1st - 2nd = ( m + 0.5 ) wavelength

2.0565 m - 1.5435 m = ( 0+ 0.5) wavelength

wavelength = 1.026 m

so here 1st min frequency will be

frequency 1 = velocity of sound / wavelength

frequency 1 = 343 / 1.026 =334.30 Hz

and

2nd min frequency will be

frequency 2 =

2.0565 m - 1.5435 m = ( 1 + 0.5) wavelength

wavelength = 0.342 m

frequency 2 = velocity of sound / wavelength

frequency 2 = 343 / 0.342 = 1002.92 Hz