Two loudspeakers 6.0 m apart are playing the same frequency. If you stand 12.0 m in front of the plane of the speakers, centered between them, you hear a sound of maximum intensity. As you walk parallel to the plane of the speakers, staying 12.0 m in front of them, you first hear a minimum of sound intensity when you are directly in front of one of the speakers. Part A)What is the frequency of the sound? Assume a sound speed of 340 m/s. I got 120.02 Hz. This is right, I checked. Part B)If you stay 12.0 m directly in front of one of the speakers, for what other frequencies between 100 Hz and 700 Hz is there a minimum sound intensity at this point?Express your answer numerically. If there is more than one answer, enter your answers in ascending order separated by commas.

The three frequencies between 100 and 700 Hz for minimum sound are

120.02 Hz, 360.06 Hz and 600.1 Hz

Explanation:

A) First of all, at the starting point centred between the speakers, as the sound is at a maximum, it means the speakers are in phase.

Thus,

When standing exactly in front of one speaker, you are 12 m from that speaker, and

√(6² + 12²) = 13.4164m from the other speaker.

Now,for minimum sound, the speakers must be out 180 degrees out of phase.

Thus; 13.4164 - 12 = 1.4164 m is an even multiple of half wavelengths of the sound.

The wavelength of sound is gotten from λ*F = V where λ is the wavelenth in m, F is the frequency in Hz, and V is the speed of sound in m/s.

So a half wavelength (H) = λ/2

So,

2H*F/(2n + 1) = V

F = (2n + 1)*V/(2H)

where n is an integer.

So,

The lowest frequency is when n = 0

Thus,

F = V/(2H)

F = 340/(2*1.4164) = 120.02 Hz

B) The next will be when n = 1

(2n + 1) = 3

F = 3 * 120.02 = 360.06 Hz

At n = 2

F = 5*120.02 = 600.10 Hz

Thus, The three frequencies between 100 and 700 Hz for minimum sound are

120.02 Hz, 360.06 Hz and 600.1 Hz