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?

1 Answer
Mar 21, 2018

#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")#