To practice Problem-Solving Strategy 16.1 Standing waves. An air-filled pipe is found to have successive harmonics at 805 Hz , 1035 Hz , and 1265 Hz . It is unknown whether harmonics below 805 Hz and above 1265 Hz exist in the pipe. What is the length of the pipe

0.213m

Explanation: The fundamental frequency is 805Hz.

The second harmonic (first overtone ) is 1035 Hz and the third harmonic (second overtone) is 1265 Hz.

The pipe is an air filled hence it is a closed pipe

Recall that v = f λ

At fundamental frequency

Where v = speed of sound in air (v) = 343 m/s

Fundamental frequency (f) = 805 Hz

Wavelength ( λ) = ?

By substituting the parameters, we have that

343 = 805 × λ

λ = 343 / 805

λ = 0.426m

The pipe is an open one and at the fundamental frequency, hence the relationship between wavelength ( λ) and length of air is given as

L = λ/4

But λ = 0.426m

L = 0.426/2

L = 0.213m

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