The graph below shows a snapshot in time (call this time t = 0) of the pressure
ID: 1630221 • Letter: T
Question
The graph below shows a snapshot in time (call this time t = 0) of the pressure difference as a function of position for two sound waves traveling through the same medium at the same time. Analyze these two waves (and, eventually, the total wave) by answering the questions below. 1) Of the various parameters (A, T, lambda, phi, and v) that are used to describe the space and time dependences of these two waves, which are different and which are the same? Explain. Find values for the parameters A, T, lambda, and v, assuming the sounds are traveling through the air in the DL room, for each wave. 2) Identify locations in space (values of x) where the interference is constructive and locations where it is destructive. 3) Suppose the sound waves are both traveling to the right. As time goes on, what happens (in general, not specifically) to the locations of the constructive and destructive interference? 4) Now suppose you are standing at x = 1600 m listening to these waves. What will you hear (i.e. how is the constructive and destructive interference manifested)?Explanation / Answer
(a) Amplitude (A) is constant or same for both the waves.
for first wave (solid line) 200=2.25 lambda ==> lambda=88 m
for second wave (dashed line) 200=2 lambda ==> lambda=100 m
Amplitude = 2.5 Pressure units
Phase angle= distance between points/wave length x 2 pi
= 100/88 * 2 *3.14
7.13 for the second wave.
(b) Constructive interference: x=20, 630, 1240
destructive interference: x=1500
(c) the locations of constructive and destructive interference will move to the left as the second wave is slightly ahead of the phase in comparison to the first wave.
(d) at x=160 m the two waves are exactly out of phase so total destructive inteference will happen and you will not hear anything.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.