Question

Organ pipe A, with both ends open, has a fundamental frequency of 475 Hz. The third harmonic of organ pipe B, with one end open, has the same frequency as the second harmonic of pipe A. Use 343 m/s for the speed of sound in air. How long are (a) pipe A and (b) pipe B?

Answer 1

The length of organ pipe A is
`L = 0.3611 \ m`

The length of organ pipe B is
`L_b = 0.2708 \ m`

Step-by-step explanation:

From the question we are told that

The fundamental frequency is
`f = 475 Hz`

The speed of sound is
`v_s = 343 \ m/s`

The fundamental frequency of the organ pipe A is mathematically represented as

`f= (v_s)/(2 L)`

Where L is the length of organ pipe

Now making L the subject

`L = (v_s)/(2f)`

substituting values

`L = (343)/(2 *475)`

`L = 0.3611 \ m`

The second harmonic frequency of the organ pipe A is mathematically represented as

`f_2 = (v_2)/(L)`

The third harmonic frequency of the organ pipe B is mathematically represented as

`f_3 = (3 v_s)/(4 L_b )`

So from the question

`f_2 = f_3`

So

`(v_2)/(L) = (3 v_s)/(4 L_b )`

Making
`L_b` the subject

`L_b = (3)/(4) L`

substituting values

`L_b = (3)/(4) (0.3611)`

`L_b = 0.2708 \ m`