Question

Organ pipe A, with both ends open, has a fundamental frequency of 350 Hz. The third harmonic of organ pipe B, with one end open, has the same frequency as the second harmonic of pipe A. How long are (a) pipe A and (b) pipe B? (Take the speed of sound to be 343 m/s.)

(a) How long is pipe A?
m
(b) How long is pipe B?
m

Answer 1

0.49 m

0.3675 m

Step-by-step explanation:

f = Frequency

L = Length

The fundamental length is given by

`L=(\lambda)/(2)\\\Rightarrow L=(v)/(2f)\\\Rightarrow L=(343)/(2* 350)\\\Rightarrow L=0.49\ m`

The second harmonic is has
`L_a=\lambda=0.49\ m`

The length of pipe A is 0.49 m

Frequency is given by

`f=(v)/(L)\\\Rightarrow f=(343)/(0.49)\\\Rightarrow f=700\ Hz`

For third harmonic n = 3

`v=\lambda f\\\Rightarrow v=(4)/(3)L_bf\\\Rightarrow L_b=(3v)/(4f)\\\Rightarrow L_b=(3* 343)/(4* 700)\\\Rightarrow L_b=0.3675\ m`

The length of pipe B is 0.3675 m