You are listening to a speaker on a tripod in a room with a nice smooth…

You are listening to a speaker on a tripod in a room with a nice
smooth marble floor, as shown in the figure below. The speaker
emits sound of wavelength (lambda). The speaker s and your ear e
are the same distanceh above the floor. Your ear and the speaker
are a distance d = 4 h away from one another.

Not only does your ear sense the sound wave moving along path 1,
but your ear also senses the sound wave that is reflected off of
the floor along path 2. The angle (theta) at which the sound hits
the floor is the same as the angle (theta) at which sound is
reflected from the floor.

(a) What is the phase difference (phi) between the two waves
when they reach your ear at point e? Express your final answer in
terms of the symbols h, (lambda), and numerical constants as
needed.

(b) Assuming that h = 1.8 m, what is the highest audible
frequency f that will result in completely destructive interference
at point e? (Note: humans can hear sounds from 20 Hz to 20
kHz.)

(c) Suppose that when the sound wave reflects off of the marble
floor, it picks up a phase shift of (pi)… or, if you prefer, a
shift of (lambda)/2. In this case, what is the highest audible
frequency f that will result in completely destructive interference
at point e?


You are listening to a speaker on a tripod in a ro

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