Embed Size (px)
Citation preview
© Manhattan Press (H.K.) Ltd. 1
10.7 Stationary waves in 10.7 Stationary waves in an open pipean open pipe
© Manhattan Press (H.K.) Ltd. 2
10.7 Stationary waves in an open pipe (SB p. 153)
Stationary waves in an open pipe
Open pipe- both ends open
particles vibrate with maximum amplitude
(antinode)
particles vibrate with maximum amplitude
(antinode)
no displacement (node)
© Manhattan Press (H.K.) Ltd. 3
10.7 Stationary waves in an open pipe (SB p. 154)
Stationary waves in an open pipe
2
22
o
o
o
vf
fv
o1
11
2 fvf
fv
o2
22
323
23
23
fvf
fv
Notes of frequencies fo, 2fo, 3fo... formed
© Manhattan Press (H.K.) Ltd. 4
10.7 Stationary waves in an open pipe (SB p. 154)
Stationary waves in an open pipe
Note: If the end corrections are considered, then for the fundamental note:
cvf
fvc
22
222
o
o
o
Go to
Example 10Example 10
Go to
Example 11Example 11
© Manhattan Press (H.K.) Ltd. 5
End
© Manhattan Press (H.K.) Ltd. 6
Q:Q: An organ pipe is 0.33 m long, open at one end
and closed at the other. Assuming that end corrections are negligible and the speed of sound is 330 m s–1, calculate(a) the frequencies of the fundamental and the first overtone, and(b) the length of a pipe which is open at both ends and has a fundamental frequency equal to the difference of the frequencies calculated in (a).
Solution
10.7 Stationary waves in an open pipe (SB p. 155)
© Manhattan Press (H.K.) Ltd. 7
Solution:Solution:
Return to
TextText
m 330
5002330
22 then pipe,open theoflength If
Hz 500 pipeopen theoffrequency lfundamenta theHence Hz 500250750 (b)
Hz 7503 overtonefirst theoffrequency The
Hz 2503304
330Frequency
440.33 l,fundamenta For the (a)
o
o
o
o1
o1
o
o
o
.'f
v''f
ff
ff.
f
fv
10.7 Stationary waves in an open pipe (SB p. 155)
© Manhattan Press (H.K.) Ltd. 8
Q:Q: An open pipe has a fundamental frequency of
300 Hz. The first overtone of a closed pipe has the same frequency as the first overtone of the open pipe. What is the length of each pipe? Assume that end corrections are negligible and the speed of sound in air is 330 m s–1.
Solution
10.7 Stationary waves in an open pipe (SB p. 156)
© Manhattan Press (H.K.) Ltd. 9
Solution:Solution:
Return to
TextText
m 413060043303
43
43 and
Hz 600 overtonefirst offrequency pipe, closed For theHz 60030022frequency overtone,first For the
m 5503002
33022
mode, lfundamenta in the pipeopen For the
112
1
o1
o
o1
.'fv'
'fff
.fv
10.7 Stationary waves in an open pipe (SB p. 156)
