Assume that your shower is 2.40 m (about 7.89 ft ) tall and can be modeled as a

Question

Assume that your shower is 2.40 m (about 7.89 ft ) tall and can be modeled as a stopped organ pipe.

Part A

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

Express your answer as "nodes" or "antinodes".

nodes

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Part B

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

Express your answer in meters to three significant figures.

4.80

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Part C

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

Express your answer in Hertz to three significant figures.

32.6

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Part D

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

Express your answers in meters to three significant figures.

6.4

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Part E

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

Express your answers in Hertz to three significant figures.

161

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4.80

Explanation / Answer

a) Nodes. Because at closed ends we have nodes in organ pipes

b) here fundamental harmonic is given by

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

so , lamda = 2.4*2 = 4.8 m

c) we have speed of sound = 343.3 m/s at room temp.

so v = lamda*frequency

so frequency = v/lamda

                      = 343.3/4.8 = 71.5 Hz , depends on temperature as sound's speed changes

d) 1st overtone : L=1*lamda

so          lamda(1) = 2.4m

2nd overtone : L=1.5*lamda

So   lamda = 2.4/1.5 = 1.6 m

e) 1st overtone

we have f = (2/2L)*v

so           f1 = (1/2.4)*343.3 = 143 Hz

2nd overtone

      f2 = (3/2L)*v

so f2=(3/4.8)*343.3 = 214.6 Hz

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