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 C

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

Express your answer in Hertz to three significant figures.

_________

Part D

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

Express your answers in meters to three significant figures.

Part E

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

Express your answers in Hertz to three significant figures.

ffund =

_________

Hz  

Explanation / Answer

C.

Assuming the speed of sound is 343 m/s, then
f = v / = 343m/s /

assuming we're talking about an organ pipe closed at one end (not all of them are!).

In the case of a system with two different ends (as in the case of a tube open at one end), the closed end is a node and the open end is an antinode. The first resonant frequency has only a quarter of a wave in the tube. This means that the first harmonic is characterized by a wavelength four times the length of the tube

_n = 4*L / n


fundamental = 4 * 2.4m / 1 = 9.60 m

f = v / = 343m/s / 9.60m = 32.6 Hz

part D

third harmonic _3 = 2 / 3 = 6.4 m

part E

f_3 = 3*343m/s / 6.4m = 160.78 Hz

If you know the speed of sound to be some other value, then use that.

Harmonics for a system with two different ends*

* such as a pipe with one end open and one end closed
†In this case only the odd harmonics resonate, so n is an odd integer.

Harmonic number Overtone number F = = F1 First harmonic --- F1 = v/4L 1 = 4L F2 Third harmonic First overtone F2 = 3F1 2 =21/3 F3 Fifth harmonic Second overtone F3 = 5F1 3 = 21/5 Fn Nth harmonic† (Nth - 1)/2 overtone F(n-1)/2 = nF1 n = 1/n

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