This is a 1-d problem. Speakers are on the x-axis at x = 4.0 m and x = 9.0 m. Th
ID: 1582471 • Letter: T
Question
This is a 1-d problem. Speakers are on the x-axis at x = 4.0 m and x = 9.0 m. The temperature is 0.0 °C. The speakers emit sound with a frequency of 82.75 Hz.
a. Determine the speed of sound at this temperature.
b. Determine the wavelength.
c. Find all locations along the x-axis between the speakers where constructive interference occurs (the location of either speaker is not allowed).
d. Find all locations along the x-axis between the speakers where destructive interference occurs (the location of either speaker is not allowed).
e. Find two locations along the x-axis between the speakers where neither constructive nor destructive interference occurs (the location of either speaker is not allowed) Classify locations on the x-axis with x < 4 as consistently having constructive interference, destructive interference, neither, or some combination of the three. Provide evidence for your assertion. Don't argue with the premise of the question.
f. Sound does reach these locations from both speakers. Classify locations on the x axis x > 9.0 as consistently having constructive interference, destructive interference, neither, or some combination of the three. Provide evidence for your assertion. Don't argue with the premise of the question. Sound does reach these locations from both speakers.
Explanation / Answer
a)We know that the speed of the sound at any temp is given by
Vs = sqrt (gamma R T/m)
Vs = sqrt (1.4 x 8.3 x 273.15/29 x 10^-3) = 331 m/a
Hence, Vs = 331 m/s
b)we have, f = 82.75 Hz
v = f lambda => lambda = v/f
lambda = 331/82.75 = 4 m
Hence, lamda = 4 m
c)consition for constructive interference
PD = 0, lambda , 2 lambda
with lambda = 4 m
Points = 0, 4
d)for destructive interference
PD = lambda/2 ; 3 lamnbda/2...
x = 4/2 = 2
x = 3 x 4/2 = 2
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