An organ pipe open at both ends has a radius of 4.0 cm and a length of 6.0 m. what is the frequency (in hz) of the third harmoni

Question

3 months ago

14

c? (assume the velocity of sound is 344 m/s.)

1 answer:

inna [3.1K] · Answer 1 · 2026-03-24T09:12:14+03:00

When air is forced into the open pipe,

L = $\frac{nλ}{2}$

where n represents any whole number such as 1,2,3,4, etc., and λ denotes the wavelength of the oscillation

This implies λ= $\frac{2L} {n}$

It is important to note that n=1 corresponds to the fundamental frequency, n=2 corresponds to the first harmonic, and so forth.

Thus, the third harmonic will be for n=4

With L=6m and n=4, solving for λ yields:

λ= $\frac{(2)*(6)}{4}$ =3m

The connection between frequency (f), sound speed (c), and wavelength (λ) is given by:

c=f.λ or f= $\frac{c}{λ}$

Therefore, f= $\frac{344}{3}$

≈115 Hz