(A) The two speakers in the drawing below are vibrating in phase, and the listen

Question

(A) The two speakers in the drawing below are vibrating in phase, and the listener is standing at point P. If the speed of sound is 343 m s-1, determine whether constuctive or destructive interference occurs at P when both speakers produce sound waves of frequency (i) 1466 Hz and (ii) 977 Hz.

speakers are sepearted by a distance of 3M , point P is veritcally 2.2 above midpoint of the speakers

(B)

A Tube, of length 30 cm, is closed at one end, and produces a sound at the fundamental frequency of 270 Hz. A higher frequency sound is produced at the third harmonic in a second Tube, which is open at both ends. When the two sounds are produced together, a beat frequency of 5 Hz is heard. Calculate the length of the second tube

Explanation / Answer

A) I'm not sure I understand the first question, because if both speakers are
equidistant from point P, then they will be in phase regardless of frequency.
B) Let y1 = wavelength of closed tube
L1 = .3 = 4 y1 = 1.2 m   since y1 = L1 / 4   for closed tube
v = f1 * y1 = 270 * 1.2 = 324 m / sec     speed of sound
Then f2 = 275 since the beat frequency is 5
For the third harmonic of an open tube
L2 = 3 * y2 / 2     since harmonics occur at N * L / 2
So y2 = v / f2 = 324 / 275 = 1.18 m
L2 = 3 * 1.18 / 2 = 1.77 m

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