Question

A fifth harmonic standing wave is set up in a closed-ended pipe that is 1.4 m long. If the frequency of the wave is 239 Hz, what is its velocity?

Answer 1

`v=268m/s`

Explanation:

It's important to remember our two formulas for open-ended pipes and closed-ended pipes when it comes to finding frequency in terms of harmonics:

Open-ended pipes: `color(blue)(f=(1)((velocity)/(2L)))`
Closed-ended pipes: `color(blue)(f=(1)((velocity)/(4L)))`

Obviously, we'll disregard the first formula for this problem, but it's important to remember both. That being said, let's plug in what we're given:

`239"Hz" = (5)((velocity)/(4(1.4"m")))`

`47.8"Hz" = ((velocity)/(4(1.4"m")))` `color(blue)((239"Hz")/(5)=47.8"Hz"`

`47.8"Hz"=((velocity)/(5.6"m"))` `color(blue)(4*1.4"m"=5.6"m")`

`velocity=267.68m/s` `color(blue)(" 47.8Hz"*5.6"m"=267.68m/s)`

`velocity=268m/s` `color(blue)("Assuming 3 significant figures")`