Question

Chapter 1 - Vibrations and Waves 1-12 y = -4 cos(3t) sin(x) y<sub>1</sub>,y<sub>2</sub>, y (cm) 4 t = 0 2 0 0 ? 2? x (cm) -2 -4 y<sub>1</sub> or y<sub>2</sub> (same) y = y<sub>1</sub> + y<sub>2</sub> y<sub>1</sub>,y<sub>2</sub>, y (cm) 4 t = T/4 2 y<sub>1</sub> 0 0 ? 2? x (cm) -2 y<sub>2</sub> -4 y = y<sub>1</sub> + y<sub>2</sub> = 0 y<sub>1</sub>,y<sub>2</sub>, y (cm) 4 t = T/2 y = y<sub>1</sub> + y<sub>2</sub> 2 0 ? 2? x (cm) -2 y<sub>1</sub> or y<sub>2</sub> -4 y<sub>1</sub>,y<sub>2</sub>, y (cm) 4 t = 3T/4 2 y<sub>2</sub> 0 0 ? 2? x (cm) y<sub>1</sub> -2 -4 y = y<sub>1</sub> + y<sub>2</sub> = 0

          Chapter 1 - Vibrations and Waves
1-12
y = -4 cos(3t) sin(x)
y<sub>1</sub>,y<sub>2</sub>, y (cm)
4
t = 0
2
0
0
?
2? x (cm)
-2
-4
y<sub>1</sub> or y<sub>2</sub> (same)
y = y<sub>1</sub> + y<sub>2</sub>
y<sub>1</sub>,y<sub>2</sub>, y (cm)
4
t = T/4
2
y<sub>1</sub>
0
0
?
2? x (cm)
-2
y<sub>2</sub>
-4
y = y<sub>1</sub> + y<sub>2</sub> = 0
y<sub>1</sub>,y<sub>2</sub>, y (cm)
4
t = T/2
y = y<sub>1</sub> + y<sub>2</sub>
2
0
?
2? x (cm)
-2
y<sub>1</sub> or y<sub>2</sub>
-4
y<sub>1</sub>,y<sub>2</sub>, y (cm)
4
t = 3T/4
2
y<sub>2</sub>
0
0
?
2? x (cm)
y<sub>1</sub>
-2
-4
y = y<sub>1</sub> + y<sub>2</sub> = 0

Show more…

Chapter 1 - Vibrations and Waves
1-12
y = -4 cos(3t) sin(x)
y<sub>1</sub>,y<sub>2</sub>, y (cm)
4
t = 0
2
0
0
?
2? x (cm)
-2
-4
y<sub>1</sub> or y<sub>2</sub> (same)
y = y<sub>1</sub> + y<sub>2</sub>
y<sub>1</sub>,y<sub>2</sub>, y (cm)
4
t = T/4
2
y<sub>1</sub>
0
0
?
2? x (cm)
-2
y<sub>2</sub>
-4
y = y<sub>1</sub> + y<sub>2</sub> = 0
y<sub>1</sub>,y<sub>2</sub>, y (cm)
4
t = T/2
y = y<sub>1</sub> + y<sub>2</sub>
2
0
?
2? x (cm)
-2
y<sub>1</sub> or y<sub>2</sub>
-4
y<sub>1</sub>,y<sub>2</sub>, y (cm)
4
t = 3T/4
2
y<sub>2</sub>
0
0
?
2? x (cm)
y<sub>1</sub>
-2
-4
y = y<sub>1</sub> + y<sub>2</sub> = 0

Added by Melissa C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Kai Chen

12/16/2019

Step 1

y = y1 + y2 y = 2sin(3t - x) - 2sin(3t + x) y = 2sin(3t - x) + 2sin(x) (since sin(-θ) = -sin(θ)) y = 2(sin(3t - x) + sin(x)) y = 2(2sin(2t)cos(x)) (using the sum-to-product trigonometric identity) y = 4cos(3t)sin(x) Show more…

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Two wave trains of the same frequency, speed, and amplitude are traveling in opposite directions along a string: y1 = 2 sin(3t - x) y2 = -2 sin(3t + x) where y, and x are in centimeters, and t is in seconds. Write the equation of the resultant standing wave, and plot the three waveforms at times t = 0, T/4, T/2, 3T/4, and T where T is the period. 1-12 y = -4cos(3t)sin(x) y1, y2, y (cm) Chapter 1 - Vibrations and Waves 1-12 y = -4cos(3t)sin(x) y1, y2, y (cm) 2 y or y same = y + y y1, y2, y (cm) 4 t = T/4 2x (cm) y1, y2, y (cm) t = T/2 = y1 + y2 2r cs) y, y2, y (cm) = 3T/4 2x (cm) = y + y = 0

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Transcript

00:01 So in this question, we have two sinusoidal wave and they have the same amplitude.

00:05 Both of them have the amplitude of 9mm and they have the same worthness.

00:10 They're pretty much just like the same side wave, but with a different face.

00:17 So they are traveling together along the string and they are pictured onto this figure.

00:25 And figure 1638 is a figure on the book.

00:29 Now i have this valley called value a.

00:34 So it's when it travels in the negative direction of the x -axis by a distance of 50 cm in 8 milliseconds.

00:46 So that is telling us the speed of traveling.

00:50 So when value a is traveling like that, the tick marks along the axis are separated by 10 centimeters.

00:57 So every one of these is 10 centimeters.

00:59 So let's the equation for one wave be of the form of ym, sine kx plus or minus omega t plus 51, or 5 1 and 0.

01:17 And then for the equation for the other wave, what are the ym, k omega, phi, and the sign.

01:37 Okay, so firstly, it is apparent that they have the same amplitude.

01:46 So this amplitude of the second wave is also 9mm.

01:51 We can also look at k.

01:53 In order to do k, we have to read out the lambda because k equals 2 pi over lambda.

02:01 And each tick is 10 cm.

02:03 Here we have 1, 2, 3, 4.

02:08 Like this in a pyramid and that is 4 tick.

02:11 So that is 40 centimeters.

02:14 So we have 2 pi over 40 centimeter...

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