Final answer:
The frequency of the sound waves is 1030.3 Hz, calculated using the wavelength that corresponds to the distance where maximum sound intensity is heard again. The phase difference between the speakers is π radians.
Step-by-step explanation:
To determine the frequency of the sound waves emitted by the speakers, we can use the phenomenon of constructive interference and the concept of sound wave interference. Constructive interference occurs when two waves combine to make a wave with a larger amplitude, which happens at the positions of maximum sound intensity that the listener hears.
Given that the sound intensity reaches a maximum again when speaker 1 is moved from 0.540 m to 0.870 m, we can deduce that this distance, 0.330 m, corresponds to one wavelength (λ) since this is the distance needed for speaker 1 to be 'in phase' again with speaker 2.
Using the wave equation v = fλ, where v is the velocity of sound and f is the frequency, we can solve for the frequency:
f = v / λ
f = 340 m/s / 0.330 m
f = 1030.3 Hz
For the phase difference between the speakers, when speaker 1 is at 0.540 m, it is λ / 2 out of phase with speaker 2 at the origin because it is at a position of constructive interference, and moving it half a wavelength results in another constructive interference. This translates to a phase difference of π radians (180°).