Question

Two speakers and are apart. the speakers emit sound of the same frequency and are in phase with each other. a person standing at point hears a maximum (constructive interference) in sound level.

(a) what is the lowest possible frequency emitted by the speakers?
(b) what is the lowest possible frequency emitted by the speakers, if the two speakers are out of phase?

Answer 1

The lowest frequency for in-phase speakers relates to the condition for constructive interference, while for out-of-phase speakers, the lowest frequency corresponds to the first occurrence of destructive interference.

Step-by-step explanation:

The student's question involves the concept of wave interference, specifically with sound waves emitted by two speakers. When the speakers are in phase and at the same frequency, the point at which a person hears a maximum sound level is where constructive interference occurs. The lowest possible frequency can be found using the relationship between wave speed, wavelength, and frequency (f = v/λ), considering the distance between the speakers and the point of constructive interference.

For out-of-phase speakers, the situation is different; destructive interference occurs when the path difference is an odd multiple of half the wavelength (λ/2). To find the lowest frequency in this case, you would look for the condition where the path difference equals half the wavelength for the first minimum in sound level.