Question

Find the fundamental frequency and the frequency of the first three overtones of a pipe 55.0 cm long, if the pipe is open at both ends.

Please enter your answer as four numbers, separated with commas.

Find the fundamental frequency and the frequency of the first three overtones of a pipe 55.0 cm long, if the pipe is closed at one end.

Please enter your answer as four numbers, separated with commas.

If the pipe is open at both ends, what is the number of the highest harmonic that may be heard by a person who can hear frequencies from 20.0 Hz to 2.00×10⁴ Hz?

If the pipe is closed at one end, what is the number of the highest harmonic that may be heard by a person who can hear frequencies from 20.0 Hz to 2.00×10⁴ Hz

Answer 1

Organ pipes

open at both ends the fundamental frequency f1 = v / 2l   v speed of sound , l length of pipe

closed pipe the fundamental frequency f1 = v / 4l   v speed of sound , l length of pipe

1)   l = 55 cm = 0.55 m            f = n f1    n = 1,2,3,4,5.........

        fundamental frequency f1 = 1* 340 / (2*0.55) = 309.09 Hz

       second harmonic or first over tone f1 = 2*f1 = 2*309.09 = 618.18 Hz

       second overtone f3 = 3*f1 = 3*309.09= 927.27 Hz

       third overtone f4 = 4*309.09 =1236.36 Hz

2) closed pipe fundamental frequency f = v / 4l = 340 / 4*0.55 = 154.54 Hz

    first overtone f1 = 3f1 = 154.54*3 = 463.62 Hz

   second overtone f2 = 5f1 = 5*154.54 =772.7 Hz

third overtone f3 = 7f1 = 154.54*7 =1081.78 Hz

3) open pipe fundamental frequency f1 = 309.09 Hz

the number of the highest harmonic that may be heard by a person is 20000 Hz = n*f1

   n = 20000 / 309.09 = 64      63 rd overtone may heard

for closed pipe is        20000/ 154.54 = 129       128 th overtone may be heard