Can someone please help with physics???

Question

A pipe open at both ends has a fundamental frequency of 310 Hz when the temperature is 0°C.

(a) What is the length of the pipe?
(b) What is the fundamental frequency at a temperature of 30°C?

Answer 1

The pipe is open at both ends. The open end always forms an antinode.
Anti>>>>>Node>>>>>>Anti
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.....................L length
so for fundamental freqency
L = lamda/2 = vo / 2*n
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for other overtones there will be 2 N, 3N.... nodes inbetween along with corresponding antinodes
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[ where vo is velocity of sound at 0 deg C, n is freq]
The sound speed relation with temp is
vt = 331.4 sqrt( 1 + TC / 273 ),
v0 = 331.4 m/s
L = vo / 2*n = 331.4 / 2*310
= 0.5345 meter or 53.45 cm
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at temp 30 deg C
v(30) = 331.4 sqrt[1+(273+30)/273] = 481.3585 m/s
for fundamental
Lamda = 2 L = 2*0.5345 (m) = 1.069 m
n = v(30) / lamda = 481.3585 / 1.069
= 450.288 Hz

Answer 2

The pipe, being open, will have a length of one wavelength. Divide the speed of sound at 0°C by the frequency and you will have the length of the pipe. For (b) divide the speed of sound at 30°C by length to give the new frequency. To be more accurate you would want to apply the coefficient of thermal expansion, for which you need to know the type of pipe.