Two wave pulses A and B are moving in opposite directions, each with a speed v=2.00 cm / s . The

Two wave pulses A and B are moving in opposite directions,...

Key Concepts

Amplitude Effects

Amplitude measures the maximum displacement of a wave from its equilibrium position. In the context of wave interference, differences in the amplitudes of the interacting waves play a crucial role in determining the overall shape and intensity of the resulting wave pattern. Variations in amplitude can indicate which pulse contributes more significantly to the resultant waveform.

Wave Pulse Propagation

Wave pulse propagation refers to the movement of individual disturbances or pulses through a medium. The speed and direction of these pulses determine when and where they overlap, which is essential in predicting the resultant wave at different times. Understanding propagation helps in mapping the relative positions of moving pulses over time.

Superposition Principle

The superposition principle states that when two or more waves travel through the same medium at the same time, the resultant displacement at any point is the sum of the displacements due to each individual wave. This concept is fundamental in understanding how multiple wave pulses interact and combine, leading to phenomena such as constructive and destructive interference.

Wave Interference

Wave interference occurs when two or more waves overlap in space. Depending on their relative phases and amplitudes, the waves can add constructively to produce a larger amplitude or destructively to reduce or cancel the amplitude. This concept is key when analyzing the overlap of pulses moving in opposite directions.

Transcript

00:01 Okay, so in this question, we have two waves that are going to pass through each other, and we're supposed to draw graphs of what the resultant superimposed wave looks like at several different time values for t.

00:18 We're given what it looks like at t equals zero, and we're supposed to draw it at t equals 1, t equals 1 .5, t equals 2, t equals 2 .5, and t equals 3 seconds.

00:29 So i started with just getting a little graph and axes set up so that you don't have to watch me do that.

00:35 And i'm going to go through each of them.

00:40 The first thing that i'll do is i'll draw each wave pulse individually.

00:44 I'll draw wave pulse a, which is the taller one that starts on the left side.

00:50 I'll draw that one in red, and then i'll draw wave pulse b for each of them in blue.

00:55 So yeah.

00:56 So first is t equals one second.

01:02 So at that point, so at t equals zero, we saw the peak of wave pulse a was at six centimeters and the peak of wave pulse b was at 14 centimeters.

01:12 And since they both have a velocity of two centimeters per second, we know that the peak of a, since it's traveling right, will now be at eight centimeters instead of 6 centimeters and we know that the peak of b will be at 12 centimeters instead of at 14 since it's traveling in the other direction.

01:36 And then we can from this, we know that a drops down to 0 centimeters, 2 centimeters to either side of the peak.

01:46 So we can draw it like that.

01:47 And then b drops down similarly to 0, 2 centimeters to either side of the peak.

01:54 So right now, they're not actually superimposed on each other.

01:57 So this is just the result.

02:01 The resultant wave of the superimposed waves is just like this, where it's at six centimeters at zero.

02:11 It goes up linearly to four centimeters in the wide direction at eight centimeters in the direction, drops back down to zero, goes up to two at 12, and drops back down to zero.

02:22 At 14.

02:24 And yep, so i'm going to erase some and we'll get started with t equals 1 .5 seconds.

02:36 All right.

02:36 So now, t is equal to 1 .5 seconds.

02:44 So before we had them move two centimeters because we went from zero to one seconds, but now each of the peaks is only going to move one centimeter since we only change the time by half a second.

02:56 So a was at the peak of a was at eight centimeters before, so now it'll be at 9.

03:04 And the peak of b was at 12 centimeters before, so it'll be at 11.

03:11 So that'll be right here.

03:13 And then we can draw how they slope down to zero on either side.

03:18 So a will drop down to zero at 7 centimeters, and at 11 centimeters, and b will drop down to zero at 9 centimeters and 13 centimeters.

03:32 So now we see that they are going to superimpose on each other a bit.

03:39 And we can see that a is going to drop to zero at 11 centimeters.

03:45 So the height at 11 centimeters will just be the peak of b.

03:49 And we see that b drops to zero at 9 centimeters.

03:51 So at 9 centimeters, the height of the wave will just be the peak of a...