To practice Problem-Solving Strategy 16.1 Standing waves. An air-filled pipe is found to have successive harmonics at 800 HzHz, 1120 HzHz, and 1440 HzHz. It is unknown whether harmonics below 800 HzHz and above 1440 HzHz exist in the pipe. What is the length of the pipe

Length of the pipe = 53.125 cm

Explanation:

given data

harmonic frequency f1 = 800 Hz

harmonic frequency f2 = 1120 Hz

harmonic frequency f3 = 1440 Hz

solution

first we get here fundamental frequency that is express as

2F = f2 - f1 ... 1

put here value

2F = 1120 - 800

F = 160 Hz

and

Wavelength is express as

Wavelength = Speed : Fundamental frequency ... 2

here speed of waves in air = 340 m/s

so put here value

Wavelength = 340 : 160

Wavelength = 2.125 m

so

Length of the pipe will be

Length of the pipe = 0.25 * wavelength ... 3

put here value

Length of the pipe = 0.25 * 2.125

Length of the pipe = 0.53125 m

Length of the pipe = 53.125 cm