A half-open pipe is constructed to produce a fundamental frequency of 224 Hz when the air temperature is 15 °C. It is used in an overheated building when the temperature is 38 °C. Neglecting thermal expansion in the pipe, what frequency will be heard?

Answer 1

The first temperature is T1 =273 +15 = 288K
The speed of sound at T1 is v1=332•sqrt(T1/273) =
=332•sqrt(288/273) =341 m/s.
v= L•f.
The length of pipe is L=v1/f1=341/224=1.52 m
The second temperature is T2 =273 +38 = 311K
The speed of sound at T2 is v2=332•sqrt(T2/273) =
=332•sqrt(311/273) =354.4 m/s.
f2=v2/L=354.4/1.52=233.13 Hz