REASONING The frequency of a pipe open at both ends is given by Equation 17.4 as , where n is an integer specifying the harmonic number, v is the speed of sound, and L is the length of the pipe. This relation can be used to find L, since all the other variables are known.
SOLUTION Solving the equation above for L, and recognizing that n = 6 for the 6th harmonic, we have
L=n((v)/(2(fn)))
L=6((343m/s)/(2(257Hz)))
L=4.0038911m
An organ pipe is open at both ends. It is producing sound at its sixth harmonic, the frequency of which is 257 Hz. The speed of sound is 343 m/s. What is the length of the pipe
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