Question

Organ pipe A, with both ends open, has a fundamental frequency of 270 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
(b) pipe B

Answer 1

Organ Pipe A has both end open.

Organ Pipe B has one end open.

speed of sound, v = 343 m/s

The fundamental frequency = 270 Hz

wavelength of the pipe when both end open

λ = 2 L

we know,

`\lambda = (v)/(f)`

now,

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

inserting all the values

`L = (343)/(2* 270)`

L_A = 0.635 m

length of pipe A is equal to 0.635 m

b) since third harmonic of pipe B is equal to second harmonic of pipe A

`f_B = f_A`

`(n_BV)/(4L_B) = (n_AV)/(2L_A)`

`L_B= (2n_BL_A)/(4n_A)`

`L_B= (2* 3 * 0.635)/(4* 2)`

L_B = 0.476 m

length of pipe B is equal to 0.476 m.