Question

A hallway 3.8 m wide dead ends with a wall that has a clock right in the middle. As you stand in the hallway, also half way between the side walls, you notice that the ticking of the clock has a tonal quality, which sounds like a frequency of 249 Hz. How far are you standing from the clock? Assume that you are hearing the ticks directly, and also echoing off the walls, but not off the ceiling and floor (they absorb sound). Use 340 m/s for the speed of sound. You will need the Pythagorean theorem to relate the distances.

Answer 1

As the clock is audiable two things are happening:

1. A direct ray of sound is coming towards me
2. I am hearing sound bouncing off of middle portion of the walls between me and the clock.

These two rays creates a constructive interference maxima and I'm standing in the point of central maxima.

So the wavelength of the sound= l = 340/249 = 1.365m

Leat us say that the length of the hall is 2L, so, according to Pythagorean theorem distance that the relfected ray travels =

The path difference:

, has to be nl, n is an integer.

For the lowest order, n = 1

so,

This is a simple case of interference.