We all sound like great singers in the shower, due to standing waves. Assume tha

Question

We all sound like great singers in the shower, due to standing waves. Assume that your shower is 2.65 m (about 8.72 ft ) tall and can be modeled as an organ pipe.

a) What will we have at the floor and ceiling, displacement nodes or antinodes? Express your answer as "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 first two overtones for this shower?

e) What are the frequencies of the first two overtones for this shower?

Explanation / Answer

a.) Antinode

b.) wavelength of the fundamental harmonic for standing waves in this shower

Lambda = (4/1)*L

= 4*2.65

= 10.6 m

c.) frequency = 343/10.6 = 32.36 Hz

d) Wavelength of first overtone

Lambda=(4/3)*L

=(4/3)*2.65

=3.53 m

Wavelength of second overtone

Lambda=(4/5)*L

=(4/5)*2.65

=2.12 m

e) frequency of first overtone= 343/3.533

= 97.07 Hz

frequency of second overtone=343/2.12

=161.79 Hz ans

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