Question

Organ pipe A, with both ends open, has a fundamental frequency of 310 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.)

Answer 1

Part a)

55.3 cm

Part b)

41.5 cm

Step-by-step explanation:

Pipe A is open at both ends so the fundamental frequency of this pipe is given as

`f_o = (V)/(2L)`

here we know that

V = 343 m/s

`f_o = 310 Hz`

now we have

`310 = (343)/(2L)`

`L = 55.3 cm`

Now we also know that second harmonic of pipe A and third harmonic of pipe B has same frequency

so we will have

`(2V)/(2L_a) = (3V)/(4L_b)`

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

`L_b = (3)/(4)(55.3) = 41.5 cm`