Physics of Sound question

Question

Two identical loudspeakers emitting the same pure tones (ƒ = 343 Hz) are facing each other at a distance of 10.0 m. If the speed of sound is 343 m/s, the wavelength λ = 1m. An observer positioned in the middle between the two speakers hears constructive interference. It can be changed to destructive interference by moving ______ m towards one of the speakers.

Answer 1

Hi Caroline,

                    |<---------5.0 m-------------->|<-------------5.0 m------------>|

Loudspeaker 1------------------------------Center----------o---------------------Loudspeaker 2

                                                               |<--- L ---->|

If the path difference between the sound waves from speaker1 and speaker2 is half the wavelength at the location marked 'o' a distance L from the center towards speaker 2

path of wave1 - path of wave2 = λ/2           

           5.0 +L - (5.0 - L) =  λ/2 

           5.0 + L - 5.0 + L  =  λ/2 

                               2L  =  λ/2 

                                  L =  λ/4 

For this particular configuration, destructive interference at every quarter wavelength between the speakers.

Locations of destructive interference are λ/4 + nλ  where n is an integer.

By moving 1/4 or 0.25 meter towards one of the speakers, the observer will experience destructive interference.