Question

A pipe 0.490 m long and closed at one end is filled with an unknown gas. The third lowest harmonic frequency for the pipe is 790 Hz.

(A) What is the speed of sound in the unknown gas?
(B) What is the fundamental frequency for this pipe when it is filled with the unknown gas?
(A) Number 374 Units m/s
(B) Number 257 Units Hz

Answer 1

516.13 m/s

263.33 Hz

Step-by-step explanation:

Given:

length of the pipe closed at one end, L = 0.490 m

Third harmonic Frequency, f= 790 Hz

Wavelength of the third Harmonic is given by:

`\lambda = \frac {4}{3}L`

speed of sound in unknown gas can be calculated as follows:

`v= f\lambda\\ \Rightarrow v= f(\frac {4}{3}L)`

Substitute the values:

`v= (790)(4)/(3)(0.490) = 516.13 m/s`

Fundamental frequency is given by:

`f_1=(v)/(4L)`

Substitute the values:

`f_1=(516.13)/(4* 0.490)= 263.33 Hz`