Question

Assume that your shower is 2.80 m (about 9.21 ft) tall and can be modeled as a stopped organ pipe

A. What will we have at the floor and ceiling, displacement nodes or antinodes?

B. What is the wavelength of the fundamental harmonic for standing waves in this shower?

C. What is the frequency of the fundamental harmonic for standing waves in this shower?

D. What are the wavelengths of the second and third harmonics for this shower?

E. What are the frequencies of the second and third harmonics for this shower?

Answer 1

Solution)

a) We will have nodes because at closed ends nodes are present n organ pipies.

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b) wavelength of fundamanetal harmonic,

L=lamda/2. Simce it is closed at both ends

so , lamda=2.80 * 2=5.6 m

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c) speed of sound=343.2 m/s

We also know,

v=lamda*frequency

so frequency=v/lamda=343.2/5.6=61.28 hz (Ans)

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d) Here, first overtone

L=1*lamda

lamda(1)=2.80 m

2nd overtone

L=1.5*lamda

so

lamda=2/3*2.8=5.3/3=1.866 m (Ans)

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Acc to HOMEWORKLIB RULES, I can answer these many parts at a time.

Good luck!:)