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Building a pipe organ with open-tube pipes spanning the range from 25 hz to 19 khz will require the length of the shortest pipe to be 0.018m
What is Length?
This is defined as the measurement or extent of a substance from end to end. The formula is shown below:
L = v/f where v is speed , f is frequency
f1 = 25hz , f2 = 19khz
The length for both sides is seen below:
l1 = 343/25 = 13.72m
l2 = 343/19000 = 0.018m.
The length of the shortest pipe is therefore 0.018m.
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The frequency of a repeated event is the number of occurrences per unit of time. The length of the shortest pipe is 0.018 m.
What is the frequency?
The frequency of a repeated event is the number of occurrences per unit of time. It is also known as temporal frequency to distinguish it from spatial frequency, and ordinary frequency to distinguish it from angular frequency.
The formula of the length is given by the formula,
[tex]L=\dfrac vf[/tex]
where v is the velocity of the substance and f is the frequency.
Given that the speed of the sound in air is 343 m/sec, while the frequency is tanging from 25Hz to 19 kHz.
Therefore, the length of the pipe will be,
[tex]L=\dfrac vf\\\\L_1=\dfrac{343}{25} = 13.72\rm\ m[/tex]
[tex]L_2=\dfrac{343}{19 \times 1000} = 0.018\rm\ m[/tex]
Hence, the length of the shortest pipe is 0.018 m.
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