Question

A pipe open at both ends has a fundamental frequency of 3.00 3 102 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 30.0°C?

Answer 1

Given

the fundamental frequency of the open pipe is f1 = 300.3 Hz

and speed of wave is V1 = 331 m/s

we know that the fundamental frequency of a open pipe is  

f1 = V1/2L

300.3 = 331 /(2*L)

L = 0.5511 m

the frequency at 30 0C = 273.15+30 = 303.15 k is f2 = ?

the speed of wave at 30 0C is  

V2 = V1 sqrt(T2/T1)

V2 = 331 sqrt(303.15/273.15) m/s

V = 348.70 m/s

now the fundamental frequency at 30 0C is

f1 = v2/2*L

f1 = 348.70/(2*0.5511) Hz

f1 = 316.37 Hz