Apipe is open at both ends. the pipe has resonant frequencies of 528 hz and 660hz (among others).

find two possible values for the length of the pipe.

To develop this problem it is necessary to apply the oscillation frequency-related concepts specifically in string or pipe close at both ends or open at both ends.

By definition the oscillation frequency is defined as

Where

v = speed of sound

L = Length of the pipe

n = any integer which represent the number of repetition of the spectrum (n)1,2,3...)(Number of harmonic)

Re-arrange to find L,

The radius between the two frequencies would be 4 to 5,

Therefore the frequencies are in the ratio of natural numbers.  That is

Here f represents the fundamental frequency.

Now using the expression to calculate the Length we have

Therefore the length of the pipe is 1.3m

For the second harmonic n=2, then

Therefore the length of the pipe in the second harmonic is 2.6m