One of the harmonic frequencies of tube A with two open ends is 426 Hz. The next
ID: 1954176 • Letter: O
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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