Question

Sound source A is located at x = 0, y = 0, and sound source B is located at x = 0, y = 2.9 m. The two sources radiate coherently and in phase. An observer at x = 12.0 m, y = 0 notes that as he takes a few steps from y = 0 in either the +y or ?y direction, the sound intensity diminishes. What is the lowest frequency, and the next to lowest frequency of the sources that can account for that observation? (Enter your answers from smallest to largest.)
______kHz
______ kHz

Answer 1

The fact that the intensity diminishes as he moves in either direction shows that the intensity has a maxima at the location of observer. This happens when the path difference between the waves coming from two coherent sources is an integral multiple of the wavelength of the wave, i.e.

? = n?

n = 1,2,3 ......

For the lowest frequency,

? = ?

Also, path difference ? is given by:

BC - AC (say C is the location of the observer) = ?(12²+2.9²) - 12 = 0.345 m = ?

Thus, lowest frequency is:

? = c/? = (300000000/0.345) Hz = 868446 kHz

Second lowest frequency is for ? =2?, or ? = (?(12²+2.9²) - 12)/2 = 0.173 m

The frequency for above is:

? = c/0.173 = 1736892 kHz