A pair of speakers connected to the same sound system face each other, one at x
ID: 1702172 • Letter: A
Question
A pair of speakers connected to the same sound system face each other, one at x = 0 and the other at x = 4.50 m. If they are playing a sound with frequency 378 Hz, what are the first three points of constructive interference between the two speakers starting from x = 0? (Take the speed of sound as 343 m/s.)points
1st closest to x = 0 1.3425926
Your response differs from the correct answer by more than 100%. m
2nd closest to x = 0 1.796296
Your response differs from the correct answer by more than 100%. m
3rd closest to x = 0 2.25
Your response differs from the correct answer by more than 10%. Double check your calculations. m
I have also tried the following numbers as answers and they were also incorrect, following the way cramster solves the problem, which is in ch. 14, problem # 33:
.4537037 .9074074 1.361111
Explanation / Answer
Let y = wavelength y = 343/378 = .907 4.5 / .907 = 4.96 wavelengths between the speakers This is very close to 5 wavelengths m y + n y = 5 where m is number of wavelengths from left speaker So if m = 1 then n = 4 m = 2 then n = 3 m = 3 then n = 2 So the first three points of constructive interference would be 1 * .907 = .907 2 * .907 = 1.81 3 * .907 = 2.72 m To get an answer more accurate than this you would need to examine the value of the sine functions at points very close to those just found.