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 2.50 m (about 8.22 ft ) tall and can be modeled as an organ pipe.

Part B) What is the wavelength of the fundamental harmonic for standing waves in this shower? SOLVED: 5.00m

Part C) What is the frequency of the fundamental harmonic for standing waves in this shower? SOLVED: 68.8 Hz

Part D) What are the wavelengths of the first two overtones for this shower? (need 2 answers sepereated by a comma)

Part E) What are the frequenices of the first two overtones for this showers? (need 2 answers seperated by a comma)

I will thumbs up any answers that are correct as well as complete procedure to solving each parts!

Explanation / Answer

(CONSIDERING THE WASHROOM AS OPEN at ONE END)
= 4L / (2n - 1)

For fundamental harmonics n = 1
a) = 4*2.50 / (2 ) => =5 meter

b) considering the velocity of sound as v = 340 m/sec
we have v = n × or n = 340 / 5= 68 Hz

c) For first overtone n = 2, so = 4L / (2*2 - 1) = 4L/3 = 3.33 meters - Answer
and for second over tone n = 3, so = 4L / (2*3 - 1) = 4L/5 = 2 meters - Answer

d) For first overtone = 3.533, from v = n => n = 340 / 3.33 , or n = 102.10Hz - Answer
and for second over tone = 2.12 , so n = 340 / 2, or n = 1700 Hz - Answer

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