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

Answer: 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