One of the harmonic frequencies of tube A with two open ends is 426 Hz. The next

Question

One of the harmonic frequencies of tube A with two open ends is 426 Hz. The next-highest harmonic frequency is 497 Hz. (a) What harmonic frequency is next highest after the harmonic frequency 1136 Hz? (b) What is the number of this next-highest harmonic?
One of the harmonic frequencies of tube B with only one open end is 4900 Hz. The next-highest harmonic frequency is 5180 Hz. (c) What harmonic frequency is next highest after the harmonic frequency 700 Hz? (d) What is the number of this next-highest harmonic?

Explanation / Answer

SOLUTION: The frequency of the open pipe is,               fm = 426 Hz The frequency of the open pipe is,               fm = 426 Hz The frequency of the next harmonic is,             fm+1 = 497 Hz For an open pipe the difference in the frequency of two consecutive resonating coloumns is given by,     fm+1 - fm = v/2L v is the speed of sound L is the length of the coloumn Therefore,    v/2L = 497 Hz - 426 Hz    v/2L = 71 Hz (a) The frequency of the next resonating coloumn for 1136 HZ is,        f' =1136 Hz + v/2L        f' = 1136 Hz + 71 Hz        f' =1207 Hz _____________________________________________________________ _____________________________________________________________ (b) The number of the harmonic is,     m = 1207 Hz/71 Hz        = 17 _____________________________________________________________ _____________________________________________________________ (c)
The frequency of the closed pipe is,       fm = 4900 Hz The ferquency of the next harmonic is,    fm+1 = 5180 Hz For an open pipe the difference in the frequency of two consecutive resonating coloumns is given by,      fm+1 - fm = v/2L v is the speed of sound L is the length of the coloumn Therefore,     v/2L = 5180 Hz - 4900 Hz     v/2L =  280 Hz The frequency of the next resonating coloumn for, 700 Hz is      f' = 700 Hz + v/2L      f' = 700 Hz + 280 Hz      f' = 980 Hz _______________________________________________________________ _______________________________________________________________ (d) The number of the harmonic is, m = 980 Hz/ (280/2) Hz         =980 Hz / 140 Hz         =7                                                The frequency of the next harmonic is,             fm+1 = 497 Hz For an open pipe the difference in the frequency of two consecutive resonating coloumns is given by,     fm+1 - fm = v/2L v is the speed of sound L is the length of the coloumn Therefore,    v/2L = 497 Hz - 426 Hz    v/2L = 71 Hz (a) The frequency of the next resonating coloumn for 1136 HZ is,        f' =1136 Hz + v/2L        f' = 1136 Hz + 71 Hz        f' =1207 Hz _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ (b) The number of the harmonic is,     m = 1207 Hz/71 Hz        = 17 _____________________________________________________________ _____________________________________________________________ (c)
_____________________________________________________________ _____________________________________________________________ (c)
_____________________________________________________________ _____________________________________________________________ The frequency of the closed pipe is,       fm = 4900 Hz The ferquency of the next harmonic is,    fm+1 = 5180 Hz For an open pipe the difference in the frequency of two consecutive resonating coloumns is given by,      fm+1 - fm = v/2L v is the speed of sound L is the length of the coloumn Therefore,     v/2L = 5180 Hz - 4900 Hz     v/2L =  280 Hz The frequency of the next resonating coloumn for, 700 Hz is      f' = 700 Hz + v/2L      f' = 700 Hz + 280 Hz      f' = 980 Hz _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ (d) The number of the harmonic is, m = 980 Hz/ (280/2) Hz         =980 Hz / 140 Hz         =7                                               

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