**Traveling Wave Function and Crest Location**A traveling wave is represented by a wave function given by:\[ y(x, t) = (5.0 \, \text{cm}) \sin\left( \frac{2\pi}{3.0 \, \text{m}} \left( x - (0.20 \, \text{m/s}) t \right) \right). \]**Problem Statement:**When \( t = 0 \, \text{s} \), find the location of the first crest of this wave function on the positive side of the x-coordinate origin. The possible answer choices are:a. 0.25 m b. 0.75 m c. 1.50 m d. 3.0 m e. \(\frac{3.0}{2\pi} \, \text{m} \)**Explanation:**At \( t = 0 \, \text{s} \):\[ y(x, 0) = (5.0 \, \text{cm}) \sin\left( \frac{2\pi}{3.0 \, \text{m}} x \right). \]To find the position of the first crest, we need to find the value of \( x \) that makes the argument of the sine function equal to \( \pi/2 \), because the sine of \( \pi/2 \) is 1 (which gives us the crest).\[ \frac{2\pi}{3.0 \, \text{m}} x = \frac{\pi}{2} \]Solving for \( x \):\[ x = \frac{\pi}{2} \cdot \frac{3.0 \, \text{m}}{2\pi} = 0.75 \, \text{m} \]**Answer:**b. 0.75 m

Answered: Image /qna-images/answer/9dabebd8-f2dd-418c-9bfc-5487e78f163f.jpg

A traveling wave is represented by a wave function y(x, t)= (5.0 cm) sin (x-(0.20 m/s)t). When 3.0 m' t= 0 s, the first crest of this wave function on the positive side of the x coordinate origin is located at a. 0.25 m. b. 0.75 m. c. 1.50 m. d. 3.0 m. 3.0 m.

A traveling wave is represented by a wave function y(x, t)= (5.0 cm) sin (x-(0.20 m/s)t). When 3.0 m' t= 0 s, the first crest of this wave function on the positive side of the x coordinate origin is located at a. 0.25 m. b. 0.75 m. c. 1.50 m. d. 3.0 m. 3.0 m.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Stretched string

A stretched string is a wire which is made up of any metal that must have a larger length compared to its thickness. The ends of the wire are fixed, and when they oscillate or are plucked, it produces two reflected transverse waves of the same frequency and same amplitude. The waves or pulses are traveling in alternate directions and superimpose with one another. This waveform is named standing or stationary waves.

Question

**Traveling Wave Function and Crest Location**

A traveling wave is represented by a wave function given by:
\[ y(x, t) = (5.0 \, \text{cm}) \sin\left( \frac{2\pi}{3.0 \, \text{m}} \left( x - (0.20 \, \text{m/s}) t \right) \right). \]

**Problem Statement:**

When \( t = 0 \, \text{s} \), find the location of the first crest of this wave function on the positive side of the x-coordinate origin. The possible answer choices are:

a. 0.25 m
b. 0.75 m
c. 1.50 m
d. 3.0 m
e. \(\frac{3.0}{2\pi} \, \text{m} \)

**Explanation:**

At \( t = 0 \, \text{s} \):
\[ y(x, 0) = (5.0 \, \text{cm}) \sin\left( \frac{2\pi}{3.0 \, \text{m}} x \right). \]

To find the position of the first crest, we need to find the value of \( x \) that makes the argument of the sine function equal to \( \pi/2 \), because the sine of \( \pi/2 \) is 1 (which gives us the crest).

\[ \frac{2\pi}{3.0 \, \text{m}} x = \frac{\pi}{2} \]

Solving for \( x \):

\[ x = \frac{\pi}{2} \cdot \frac{3.0 \, \text{m}}{2\pi} = 0.75 \, \text{m} \]

**Answer:**
b. 0.75 m

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