Answer:
fb = 240.35 Hz
Explanation:
In order to calculate the beat frequency generated by the first modes of each, organ and tube, you use the following formulas for the fundamental frequencies.
Open tube:
[tex]f=\frac{v_s}{2L}[/tex] (1)
vs: speed of sound = 343m/s
L: length of the open tube = 0.47328m
You replace in the equation (1):
[tex]f=\frac{343m/s}{2(0.47228m)}=362.36Hz[/tex]
Closed tube:
[tex]f'=\frac{v_s}{4L'}[/tex]
L': length of the closed tube = 0.702821m
[tex]f'=\frac{343m/s}{4(0.702821m)}=122.00Hz[/tex]
Next, you use the following formula for the beat frequency:
[tex]f_b=|f-f'|=|362.36Hz-122.00Hz|=240.35Hz[/tex]
The beat frequency generated by the first overtone pf the closed pipe and the fundamental of the open pipe is 240.35Hz
