Question

If the fundamental frequency of a piece of conduit is 707 Hz, and the speed of sound is 343 m/s, determine the length of the piece of conduit (in m) for each of the following cases. (a) the piece of conduit is closed at one end (b) the piece of conduit is open at both ends

Answer 1

a) 0.12 m

b) 0.24 m

Step-by-step explanation:

`f_0`= Fundamental frequency = 707 Hz

Speed of sound = 343 m/s

Length of the piece of conduit

a) Closed at one end

`f_0=(v)/(4L)\\\Rightarrow L=(v)/(4f_0)\\\Rightarrow L=(343)/(4* 707)\\\Rightarrow L=0.12\ m`

Length of conduit = 0.12 m

a) Open at both ends

`f_0=(v)/(2L)\\\Rightarrow L=(v)/(2f_0)\\\Rightarrow L=(343)/(2* 707)\\\Rightarrow L=0.24\ m`

Length of conduit = 0.24 m