1. How long does an organ pipe have to be if it is closed at one end, open at th
ID: 2102769 • Letter: 1
Question
1. How long does an organ pipe have to be if it is closed at one end, open at the other, and has a fundamental frequency of 107 Hz? Assume that the speed of sound in air is 343 m/s. Your answer should be given in centimeters to the nearest centimeter.
2. A piano tuner hears a beat frequency of 5.4 Hz when comparing the piano's A-string against a reference tuning fork vibrating at 440 Hz. Assuming the piano strong has too low a pitch, what percent increase in tension is needed to bring the string into tune? You answer should be given to the nearest tenth of a percent.
Explanation / Answer
ANSWER
In a closed pipe , in fundamental mode of v vibration, the open end is antinode and closed end is node
length of pipe=L=distance between node and nearest antinode
distance between node and nearest antinode=(1/4) of wavelength
L=(1/4) of wavelength
wavelength = 4L
the fundamental frequency of organ pipe closed at one end=velocity of sound/wavelength
the fundamental frequency of organ pipe closed at one end=velocity of sound/4*length of pipe
velocity of sound=v
the fundamental frequency =fo= v/4L
L=v/4fo=v/4*241.8= v/967.2
(a) substitute value of velocity of sound at 20 degreeC to find length L of closed pipe
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