Question

A closed-end organ pipe is used to produce a mixture of sounds. The third and fifth harmonics in the mixture have frequencies of 1100 Hz and 1833 Hz respectively. What is the frequency of the first harmonic played by the organ pipe

Answer 1

`F_1=366.67Hz`

Step-by-step explanation:

From the question we are told that:

Frequency of 3rd harmonics
`F_3=1100`

Frequency of 5th harmonics
`F_3=1833`

Generally the equation for Wavelength at 3rd Harmonics is mathematically given by

`\lambda_3=(4)/(3)l`

Therefore

`F_3=(3v)/(4l)`

Generally the equation for Wavelength at 1st Harmonics is mathematically given by

`\lambda_1=(4)/(1)l`

Therefore

`F_1=(v)/(4l)`

Generally the equation for the frequency of the first harmonic is mathematically given by

`F_1=(F_3)/(3)`

`F_1=(1100)/(3)`

`F_1=366.67Hz`