Resonant Frequency and speed of sound

[Codav]

1. Hollow tube chimes are made of metal and are open at each end. One chime is 0.54m long.

-If the speed of sound is 346m/s, what is the frequency of sound produced by the third resonant length?

-What would happen to the frequency of sound produced by the third resonant length if the chime were shorter?

3. I'm having a hard time with this question, but here's my attempt:

Info: 0.54m, Speed of sound=346m/s
Half of one wavelength is the length of the chime.
λ=0.54m*2
λ=1.08m
Find frequency:
v=ƒ*λ
346m/s=ƒ*1.08m
ƒ=346/1.08
ƒ=320Hz
Find the third resonant length:
L3=5λ/4
L3=5(1.08)/4
L3=1.35m
Find frequency at this length:
ƒ=v/λ
ƒ=346m/s/1.35
=256Hz
3rd resonance frequency should be around 960Hz

 

[BvU]

L3 is still the length of the pipe, so $\lambda$ is a lot smaller than the 1.08 m you use...

The 5/4 isn't correct either: both ends are open

 

[AlephZero]

From the information given, I suppose you are meant to solve the problem like the OP did.

But in real life the frequency of a hollow tube chime depends on the vibration of the tube bending like a beam, not on the length of the air column inside.

 

[Codav]

I've solved it myself. It's actually quite simple, I was using the wrong equation for resonant frequency.

Info: 0.54m, Speed of sound=346m/s
Half of one wavelength is the length of the chime.
λ=0.54m*2
λ=1.08m
Use first resonant frequency equation:
F1=v/λ
F1=346/1.08
=320Hz
Now multiply the first resonant length frequency by 3 to achieve the third resonant length frequency.
320*3=960Hz.

 

[BvU]

Well done.