Explanation Given: The displacement is: D ( x , t ) = ( 3.0 mm ) e i ( 2.0 x + 8.0 t + 5.0 ) Formula used: The general equation of wave in a string is as follows: ∂ 2 D ∂ t 2 = v 2 ∂ 2 D ∂ x 2 Where, ∂ 2 D ∂ t 2 = Second partial derivative of displacement with respect to t. ∂ 2 D ∂ x 2 = Second partial derivative of displacement with respect to x . Calculation: In a medium, the displacement of a particle depends both on the position of the particle ( x ) and the time of observation ( t ). So, D must be a function of the two variables x and t . The given displacement D ( x , t ) = ( 3.0 mm ) e i ( 2.0 x + 8.0 t + 5.0 ) is a function of two variables x and t , hence, it represents a displacement of a particle in a medium. Check if the displacement represents a wave in motion or a traveling wave. One can do this by replacing x in Equation with x − v t . To see why this works, recall that the wave moves distance v t during time t . In other words, whatever displacement the wave has at position x at time t , the wave should have had that equal displacement at a position x − v t at the earlier time t = 0 . Mathematically, this idea can be written as D ( x , t ) = D ( x − v t , t = 0 ) D ( x , t ) = ( 3.0 mm ) e i ( 2.0 x + 8.0 t + 5.0 ) D ( x − v t , t = 0 ) = ( 3.0 mm ) e i ( 2.0 ( x − v t ) + 8.0 t + 5.0 ) = ( 3.0 mm ) e i ( 2.0 ( x − v × 0 ) + 8.0 t + 5.0 ) = ( 3.0 mm ) e i ( 2.0 x + 8.0 t + 5.0 ) = D ( x , t ) Since D ( x , t ) = D ( x − v t , t = 0 ) , the displacement represents a traveling wave. The general equation of wave in a string is ∂ 2 D ∂ t 2 = v 2 ∂ 2 D ∂ x 2 ∂ 2 D ∂ t 2 = ∂ 2 ∂ t 2 ( ( 3

Student Workbook for Physics for Scientists and Engineers: A Strategic Approach, Vol 1. (Chs 1-21)

4th Edition

ISBN: 9780134110646

Author: Randall D. Knight (Professor Emeritus)

Publisher: PEARSON

See similar textbooks

Concept explainers

Shock Waves

Shock waves are common in continuum mechanics, and their dominance is attributable to the fact that they are stronger (or even less) compressible. Substantial perturbations propagated as sudden dynamic changes of a compressible medium supersonically. Sho…

Videos

Question

Chapter 16, Problem 65EAP

To determine

Whether the displacement is a traveling wave.

To Calculate: The wave speed.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16, Problem 64EAP

Chapter 16, Problem 66EAP

Students have asked these similar questions

Certain types of particle detectors can be used to reconstruct the tracks left by unstable, fast-moving sub-atomic particles. Assume that a track with a length of L=2.97 mm in the laboratory frame of reference has been observed. Further assume that you determined from other detector data that the particle moved at a speed of L=0.910 ⚫ c, also in the laboratory frame of reference. c denotes the speed of light in vacuum. What proper lifetime would you determine for this particle from the data given? T= 4.0 S

generated worksheet

While cruising down University Boulevard you are stopped by a cop who states that you ran a red traffic light. Because you don't want to pay the stiff fine, you are attempting a physics defense. You claim that due to the relativistic Doppler effect, the red color of the light λ=616 nm appeared green '=531 nm to you. The cop makes a quick calculation of his own and rejects your defense. How fast, in terms of your speed u divided by the speed of light in vacuum c, would you have to drive to justify your claim? Note that the speed u is taken to be a positive quantity. U 4.0 C

Chapter 16 Solutions

Student Workbook for Physics for Scientists and Engineers: A Strategic Approach, Vol 1. (Chs 1-21)

Ch. 16 - Prob. 1CQ Ch. 16 - A wave pulse trath along a stretched string at a...Ch. 16 - FIGURE Q16.3 is a history graph showing the...Ch. 16 - FIGURE Q16.4 shows a snapshot graph and a history...Ch. 16 - Rank in order, from largest to smallest, the...Ch. 16 - A sound wave with wavelength ?0 and frequency...Ch. 16 - Prob. 7CQ Ch. 16 - FIGURE Q16.8 is a snapshot graph of a sinusoidal...Ch. 16 - FIGURE Q16.9 shows the wave fronts of a circular...Ch. 16 - Prob. 10CQ

Ch. 16 - One physics professor talking produces a sound...Ch. 16 - You are standing at x = 0 m, listening to a sound...Ch. 16 - The wave speed on a string under tension is 200...Ch. 16 - The wave speed on a string is 150 m/s when the...Ch. 16 - A 25 g string is under 20 N of tension. A pulse...Ch. 16 - Draw the history graph D(x = 4.0 m, t ) at x = 4.0...Ch. 16 - Prob. 5EAP Ch. 16 - Draw the snapshot graph D (x, t = 0 s) at t = 0 s...Ch. 16 - Prob. 7EAP Ch. 16 - Prob. 8EAP Ch. 16 - Prob. 9EAP Ch. 16 - A wave has angular frequency 30 rad/s and...Ch. 16 - A wave travels with speed 200 m/s. Its wave number...Ch. 16 - Prob. 12EAP Ch. 16 - The displacement of a wave traveling in thee...Ch. 16 - What are the amplitude, frequency and wavelength...Ch. 16 - 15. Show that the displacement D(x, t) cx2 + dt2,...Ch. 16 - Show that the displacement D(x, t) = ln(ax + bt),...Ch. 16 - a. What is the wavelength of a 2.0 MHz ultrasound...Ch. 16 - Prob. 18EAP Ch. 16 - Prob. 19EAP Ch. 16 - Prob. 20EAP Ch. 16 - Prob. 21EAP Ch. 16 - Prob. 22EAP Ch. 16 - 23. Cell phone conversations are transmitted by...Ch. 16 - a. How long does it take light to travel through a...Ch. 16 - A light wave has a 670 nm wavelength in air. Its...Ch. 16 - Prob. 26EAP Ch. 16 - Prob. 27EAP Ch. 16 - Prob. 28EAP Ch. 16 - Prob. 29EAP Ch. 16 - Prob. 30EAP Ch. 16 - Prob. 31EAP Ch. 16 - Prob. 32EAP Ch. 16 - A sound wave with intensity 2.0 × l0-3 W/m2 is...Ch. 16 - Prob. 34EAP Ch. 16 - Prob. 35EAP Ch. 16 - During takeoff, the sound intensity level of a jet...Ch. 16 - 37. The sun emits electromagnetic waves with a...Ch. 16 - What are the sound intensity levels for sound...Ch. 16 - Prob. 39EAP Ch. 16 - Prob. 40EAP Ch. 16 - Prob. 41EAP Ch. 16 - Prob. 42EAP Ch. 16 - A bat locates insects by emitting ultrasonic...Ch. 16 - Prob. 44EAP Ch. 16 - 45. I FIGURE P16.45 is a history graph at x = 0 m...Ch. 16 - . I FIGURE P16.46 is a snapshot graph at t=0sof a...Ch. 16 - Prob. 47EAP Ch. 16 - Prob. 48EAP Ch. 16 - Prob. 49EAP Ch. 16 - A helium-neon laser beam has a wavelength in air...Ch. 16 - Earthquakes are essentially sound waves—called...Ch. 16 - Helium (density 0.18k/m ’ at 0C and 1 atm...Ch. 16 - Prob. 53EAP Ch. 16 - 54. A sound wave is described by ,where y is in m...Ch. 16 - A wave on a string is described by...Ch. 16 - Prob. 56EAP Ch. 16 - Prob. 57EAP Ch. 16 - Prob. 58EAP Ch. 16 - Prob. 59EAP Ch. 16 - The string in FIGURE P16.60 has linear density ....Ch. 16 - A string that is under 50.0N of tension has linear...Ch. 16 - Prob. 62EAP Ch. 16 - A sinusoidal wave travels along a stretched...Ch. 16 - Prob. 64EAP Ch. 16 - Prob. 65EAP Ch. 16 - An AM radio station broadcasts with a power of...Ch. 16 - Prob. 67EAP Ch. 16 - The sound intensity 50m from a wailing tornado...Ch. 16 - Prob. 69EAP Ch. 16 - 70. A compact sound source radiates of sound...Ch. 16 - Prob. 71EAP Ch. 16 - Prob. 72EAP Ch. 16 - Prob. 73EAP Ch. 16 - Prob. 74EAP Ch. 16 - Prob. 75EAP Ch. 16 - Prob. 76EAP Ch. 16 - Prob. 77EAP Ch. 16 - A starship approaches its home planet at a speed...Ch. 16 - Prob. 79EAP Ch. 16 - Prob. 80EAP Ch. 16 - Prob. 81EAP Ch. 16 - A roof mass m and length L hangs from a ceiling....Ch. 16 - A communications truck with a 44-cm-diameter dish...Ch. 16 - Prob. 84EAP Ch. 16 - A water wave is a shallow-water wave if the water...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Whether the displacement is a traveling wave. To Calculate: The wave speed.