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