Question

Two loudspeakers in a 20 C room emit 600 Hz sound waves along the x-axis. o

a) If the speakers are in phase, what is the smallest distance between the speakers for which the interference of the sound waves creates maximum destruction?
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?

Answer 1

Answer

given,

frequency = 600 Hz

speed of sound = 343 m/s

wavelength =

$\lambda = \dfrac{v}{f}$

$\lambda = \dfrac{343}{600}$

λ = 0.572 m

for destructive interference

  path difference = $\dfrac{\lambda}{2}$

  path difference = $\dfrac{0.572}{2}$

  path difference = 0.286 m

b)

path difference will be equal to 0.286 m

the sound distance from the λ/2 from the first speaker will be out of phase  with the sound at that first speaker.

Since the second speaker is described as being out of phase with the  first, placing them λ/2 apart will make their sound constructively interfere.