Open air columns/ resonant length help

[Pruzhinkin]

Homework Statement

Hollow tube chimes are made of metal and are open at each end. One chime is 0.54 m long.
A) if the speed of sound is 346 m/s, what is the frequency of sound produced by the third resonant length?
B)What would happen to the frequency of sound produced by the third resonant length if the chime were shorter?

Homework Equations

L1 = lambda/2 or lambda = 2L
L2 = lambda
L3 = 3 * lambda/2 or lambda = 2L/ 3
f1 = v/ lambda

The Attempt at a Solution

A) Lambda = 2L = 2 x (0.54m) = 1.08 m
f1 = v/ lambda = 346m/s / 1.08m = 320.4 Hz
L3 = 3 * (1.08m)/2 = 1.62 m

answer is
f = 346 / 1.62 = 213.6 Hz

or am i supposed to used f3=3f1, or is that only for string resonance. If it is used here then f3 = 3 * 320.4 = 961.2 Hz?

B) Not quite sure here, I understand what happens if a wavelength, frequency, or speed of sound changes, but for some reason this escapes me. I think i just fell into some sort of stupor where my head barely thinks.

Thanks in advance guys!

 

[Pruzhinkin]

I think the frequency is supposed to be 320.37Hz instead of 320.4Hz. From reading into this, it appears that i do need to use f3 = 3f1 or f3=3v/2L to find the third resonant length frequency, which would give me 961.11Hz. Is this correct?
Still not sure about B)

 

[ehild]

If the frequency of the third resonant length means the frequency of the third harmonic (3 half-wavelength is there along the length of the chime), that 961 Hz is correct.

As for B: Think, what happens to the wavelength if the length of the chime decreases?

ehild

 

[Pruzhinkin]

B. The wavelength shortens and the frequency increases/ temperature of course stays the same! Did i get it right?
Thanks for verifying my answer for A.:)

 

[ehild]

It is hidden but assumed that "everything the same around, just using a shorter chime". The speed of sound is the same, so you are right, frequency = speed of sound /lambda is higher for a shorter chime. ehild