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

Answer

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,

 $\lambda = \dfrac{v}{f}$

now,

 $L = \dfrac{v}{2f}$

inserting all the values

 $L = \dfrac{343}{2\times 270}$

  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

     $f_B = f_A$

     $\dfrac{n_BV}{4L_B} = \dfrac{n_AV}{2L_A}$

     $L_B= \dfrac{2n_BL_A}{4n_A}$      

     $L_B= \dfrac{2\times 3 \times 0.635}{4\times 2}$

        L_B = 0.476 m

length of pipe B is equal to 0.476 m.