Ive been working on this ? awhile and cant figure it out please help!
The longest pipe in a certain organ is 5.82 m long.
(a) What is the lowest frequency the organ will produce if the pipe is open at both ends?
(b) What is the lowest frequency the organ will produce if the pipe is closed at one end?
The longest pipe in a certain organ is 5.82 m long.
(a) What is the lowest frequency the organ will produce if the pipe is open at both ends?
(b) What is the lowest frequency the organ will produce if the pipe is closed at one end?
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Open tubes resonate at v/2L, closed tubes at v/4L where v is the speed of sound and L is the length.
f_open=343/(2*5.82) = 29.46Hz
f_closed = 14.73Hz
f_open=343/(2*5.82) = 29.46Hz
f_closed = 14.73Hz
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You need the speed of sound. Assume 340 m/s unless otherwise specified.
If the pipe is open at both ends there is no phase reversal at either end.
A single whole wave must then exist in the total path length.
This total path length is twice the length of the pipe.
So wavelength is 11.64 m
and v = f lambda
so calculate f from this.
If the pipe is closed at one end then at that end the wave is reflected upside down.
It has a phase change equivalent to 1/2 wavelength at this point.
Now only a half a wave needs to fit into the path length
so 1/2 wavelength = 11.64 m
wavelength = 23.28 m
and the frequency will be exactly half that of the first answer above.
If the pipe is open at both ends there is no phase reversal at either end.
A single whole wave must then exist in the total path length.
This total path length is twice the length of the pipe.
So wavelength is 11.64 m
and v = f lambda
so calculate f from this.
If the pipe is closed at one end then at that end the wave is reflected upside down.
It has a phase change equivalent to 1/2 wavelength at this point.
Now only a half a wave needs to fit into the path length
so 1/2 wavelength = 11.64 m
wavelength = 23.28 m
and the frequency will be exactly half that of the first answer above.