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Sophia_6535
#1 Posted : Saturday, June 19, 2021 11:28:58 PM
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Hi,

I am having issues with this question:

Consecutive resonances occur at wavelengths of 8 m and 4.8 m in an organ pipe closed at one end. What is the length of the organ pipe? (Note: Resonances occur at L = nλ/ 4, where L is the pipe length, λ is the wavelength, and n = 1, 3, 5,…)

I understand that L = nλ/4 needs to be used but when looking at the answers the math confuses me and I become unsure of how to solve it

Answer: 6m

Any help is appreciated!
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INSTR_Calla_139
#2 Posted : Tuesday, June 22, 2021 7:34:33 PM
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Hello Sophia,

Using the equation L = nλ/4 I would start by figuring out which variables I know:

I know that these two wavelengths are occurring at n=3 and n=5 (it says they must be consecutive resonances) because these two ns workout to have the same length of pipe.

I also know that λ=8m and λ=4.8m

We are solving for L, which will be constant so you can also think about it like L=n₁*8/4=n₂*4.8/4. so of the possible n values, what multiplied by 8 will equal the same value as the next odd integer multiplied by 4.8?

L= (3*8)/4 = 6m
L=(5*4.8)/4 = 6m

Hope this helps a little bit
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