Question

If the speed of sound in the air is 340 m/s, the length of the organ pipe, open at both ends, that can resonate at the fundamental frequency of 136 Hz, would be:

Answer 1

1.25 m

Step-by-step explanation:

For an open-air pipe, the two ends of the pipe corresponds to two antinodes of the standing wave; therefore, the wavelength of the wave is equal to twice the length of the tube:

`\lambda=2 L`

We can rewrite the wavelength using the speed of the sound wave, v, and the frequency, f:

`\lambda=(v)/(f)`

And substituting into the previous equation we get

`(v)/(f)=2L\\L= (v)/(2f)`

And using

v = 340 m/s

f = 136 Hz

We find the length of the organ pipe:

`L=(340 m/s)/(2(136 Hz))=1.25 m`