Standing Waves in an Air-Filled Pipe

What harmonics are found in an air-filled pipe?

Successive harmonics at 805 Hz, 1035 Hz, and 1265 Hz are found in the air-filled pipe. Is it possible for harmonics below 805 Hz and above 1265 Hz to exist in the pipe?

Answer:

The harmonics found in the air-filled pipe are 805 Hz, 1035 Hz, and 1265 Hz. It is unknown whether harmonics below 805 Hz and above 1265 Hz exist in the pipe.

To determine the length of the pipe, we can use the formula for the fundamental frequency of a closed tube:

fn = n(v/2L)

Where fn is the frequency of the nth harmonic, v is the velocity of sound in air, L is the length of the tube, and n is the harmonic number.

Given that the fundamental frequency is 256 Hz and the velocity of sound in air is approximately 343 m/s, we can solve for the length of the pipe:

L = (v/2f1)

L = (343/2*256)

L = 0.336 m

Therefore, the length of the air column in the tube is 0.336 m.

For the second resonance (first overtone), the students will observe a length of 0.335 m.