Question

A string is tied across the opening of a deep well, at a height 5 m above the water level. The string has length 7.51m and linear density 4.17 g/m; any time there is a wind, the string vibrates like mad. The speed of sound in air is 343 m/s. Assuming that the resonance causing this vibration involves the lowest harmonics of both the string and the well, calculate the string's tension. Answer in units of N.

Answer 1

Match the fundamental lowest frequency of the string (string wave speed divided by twice the string length) to that of the well acoustic fundamental (treated as an open pipe) and solve for the tension, which will be the only unknown.

Answer 2

The well is a quarter wavelength long, compute frequency.

THen, knowing freq, mass density you can find tension from the law of strings.

Answer 3

A half wavelength actually, node both ends, antinode in the middle.

Answer 4

Oh, yes, the well is a quarter wave.

Answer 5

To elaborate on Prof Damons last remark: The water at the bottom provides a 180degree phase change, so the path up and down have to add to the other 180 degrees needed for wave reinforcement, thus 1/4 lambda length down, and 1/4 lambda up.