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Ch 15: Mechanical Waves
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 15: Mechanical WavesProblem 34b
Chapter 15, Problem 34b

Two pulses are moving in opposite directions at 1.0 cm/s on a taut string, as shown in Fig. E15.34. Each square is 1.0 cm. <IMAGE> Sketch the shape of the string at the end of 7.0 s.

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Identify the initial positions of the two pulses on the string. Assume the left pulse is at position x1 and the right pulse is at position x2.
Determine the direction of movement for each pulse. The left pulse moves to the right, and the right pulse moves to the left, each at a speed of 1.0 cm/s.
Calculate the distance each pulse will travel in 7.0 seconds. Since the speed is 1.0 cm/s, each pulse will move 7.0 cm in 7.0 seconds.
Determine the new positions of the pulses after 7.0 seconds. The left pulse will be at position x1 + 7.0 cm, and the right pulse will be at position x2 - 7.0 cm.
Sketch the shape of the string by placing the pulses at their new positions. Ensure that the pulses maintain their original shape and size as they move along the string.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Wave Superposition

Wave superposition is the principle that when two or more waves overlap, the resultant wave is the sum of the individual waves. This concept is crucial for understanding how the pulses interact as they meet on the string, affecting the shape of the string at any given time.
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Wave Propagation

Wave propagation refers to the movement of waves through a medium. In this scenario, each pulse travels at a constant speed of 1.0 cm/s in opposite directions. Understanding this helps predict the position of each pulse after a given time, which is essential for sketching the string's shape.
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Time Calculation

Time calculation involves determining the position of the pulses after a specific duration. Given the speed and direction of the pulses, calculating their positions after 7.0 seconds allows us to sketch the string's shape accurately, considering the initial positions and movement.
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Related Practice
Textbook Question

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x,t)=(2.30mm)cos[(16.98 rad/m)x+(742 rad/s)t]y(x,t)=\(\left\)(2.30\(\operatorname{mm)}\]\cos\)[\(\left\)(16.98\(\text{ }\)rad/m\(\right\))x+(742\(\text{ }\)rad/s\(\right\))t]. Being more practical, you measure the rope to have a length of 1.35 m1.35\(\text{ m}\) and a mass of 0.00338kg0.00338\(\operatorname{kg}\). You are then asked to determine the following: (f) tension in the rope; (g) average power transmitted by the wave.

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Textbook Question

Two pulses are moving in opposite directions at 1.0 cm/s on a taut string, as shown in Fig. E15.34. Each square is 1.0 cm.

<Image>

Sketch the shape of the string at the end of 6.0 s.

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At a distance of 7.00 x 1012 m from a star, the intensity of the radiation from the star is 15.4 W/m2. Assuming that the star radiates uniformly in all directions, what is the total power output of the star?

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A 1.50-m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 62.0 m/s.What are the wavelength and frequency of the second overtone?

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A 1.50-m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 62.0 m/s.What are the wavelength and frequency of the fundamental?

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