Question

5. A person hums into the top of a well and hears that standing waves are established at frequencies of 42, 70, and 98 Hz. She happens to have a tuning fork with her. The 42 Hz frequency sound is not the fundamental (n 1) frequency. How deep is the well? Va 343 m/s. Hint: Overtones are the n > 1 multiples of the fundamental frequency. Determine the n 1 frequency of the well whch results in the given overtones. The fundamental is not 42 Hz. Overtone frequencies are divisible by the fundamental frequency in accordance with n - 1,3, and 5. For example, for a fundamental frequency of fi -100 Hz, the standing waves or an open-closed tube would produce frequencies of 300 Hz, 500 Hz, 700 Hz, etc. Variables n and m are interchangeable. Frequencies that occur in an open-closed air column such as the well are given by the equation. Solve for L: -"(%) n where n 1,3, 5 where n-1,3, s

Answer 1

f=nv/4L equation

so you take two of the frequencies given and divide them to solve for n

42 = nv/4L and

70 = (n+2)v/4L.....divide these two equations and solve for n....you should get n=3

plug that back into f=nv/4L...and solve for L

=> L = nv/4f

= (3*343)/(4*42)

= 6.125 m