Two loudspeakers in a 20 ∘ C room emit 686 Hz sound waves along the x-axis.a. If the speakers are in phase, what is the smallest distance between the speakers for which the interference of the sound waves is maximum destructive? b. If the speakers are out of phase, what is the smallest distance between the speakers for which the interference of the sound waves is maximum constructive?

Question

Two loudspeakers in a       20          ∘        C room emit 686 Hz sound waves along the x-axis.a. If the speakers are in phase, what is the smallest distance between the speakers for which the interference of the sound waves is maximum destructive? b. If the speakers are out of phase, what is the smallest distance between the speakers for which the interference of the sound waves is maximum constructive?

yassou1v · Accepted Answer

(a) lf the loudspeakers emit sOund in phase and along the same direction, then to have a perfect destructive interference the minimum distance will have to be half the wavelength. This distance will be  d  =      λ    2    =      v          2      f        =      345          2      ∗      686        =  25.1  c  m(b) In this case the distance will be the same, assuming the phase difference is   π.Result:25.1 cm

popljuvao69 · Accepted Answer

Wavelength of the sound waves emitted by the speakers is:  λ  =      v    f    =      343    686    =  0.5  mThe destructive interference condition is:  △  d  =  (  m  +      1    2    )  λ where m=0,1,2,3,...For, minimum path difference, the value of the integer is equal to zero:  △  d  =      λ    2    =      0.5    2    =  0.25  mResult:0.25m

Answered question

Answer & Explanation

New Questions in Wave motion