You have a pipe with one end closed; you can adjust its height. Next to the pipe

Question

You have a pipe with one end closed; you can adjust its height. Next to the pipe, you have a 57.0  cm,   9.73 g wire under a tension of 4000 N. You'd like to adjust the length of the pipe so that, when it produces sound at its fundamental frequency, this sound causes the wire to vibrate in its second overtone with very large amplitude. If you need it, use 344 m/s for the speed of sound in air.

How long should the pipe be? In meters

I have been looking at other chegg posts and following along but I cannot seem to get the right answer, please help!

Explanation / Answer

Speed of wave in the wire = t.l/m = 4000 . 0.57 / 9.73 . 10^–3

= 484.073m/s

Wavelength of the 2nd overtone = 0.57 . 2/3 = 0.38 m

Frequency of 2nd overtone = 484.073 / 0.38 = 1273.8 Hz

The pipe must produce this note using air with a speed of sound = 344 m/s

So wavelength of the sound will be 344 / 1273.8 = 27.0 cm

The length of pipe that will produce this note as its fundamental is wavelength/4 =27/4 = 6.75 cm = 0.0675 m

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.