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23 Nov 2019

Why does charge/area = current/(width*speed)? I'm guessing that it's because the "area" would be a traveling wave of particulate matter? Would that be correct?

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Casey Durgan
Casey DurganLv2
23 Nov 2019

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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

How does the equation for displacement differ between a traveling wave and simple harmonic motion. Why is the formula for the velocity in simple harmonic motion so different from the one for the speed of the wave in traveling waves? When a wave travels, what is moving and how?

Two transverse standing waves are shown in the drawing below.The strings have the same tension and length, but the bottom stringis more massive. Which standing wave, if either, is vibrating atthe higher frequency?
a. The top standing wave has the higher frequency because thetraveling waves have a smaller speed due to the smaller mass of thestring.
b. The top standing wave has the higher frequency, because thetraveling waves have a larger speed due to the smaller mass of thestring.
c. Both standing waves have the same frequency, because thefrequency of vibration does not depend on the mass of thestring.
d. The bottom standing wave has the higher frequency, becausethe traveling waves have a smaller speed due to the larger mass ofthe string.
e. The bottom standing wave has the higher frequency, becausethe traveling waves have a larger speed due to the larger mass ofthe string.

Consider a traveling wave described by the formula

y_1(x,t) = A \sin(k x - \omega t).

This function might represent the lateral displacement of a string, a local electric field, the position of the surface of a body of water, or any of a number of other physical manifestations of waves.

Part A  
Which one of the following statements about the wave described in the problem introduction is correct?
ANSWER:
  The wave is traveling in the +x direction.
The wave is traveling in the -x direction.
The wave is oscillating but not traveling.
The wave is traveling but not oscillating.		  
Part B  
Which of the expressions given is a mathematical expression for a wave of the same amplitude that is traveling in the opposite direction? At time t=0 this new wave should have the same displacement as y_1(x,t), the wave described in the problem introduction.
ANSWER:
  A \cos (k x - \omega t)
A \cos (k x + \omega t)
A \sin (k x - \omega t)
A \sin (k x + \omega t)		  

 

 

The principle of superposition states that if two functions each separately satisfy the wave equation, then the sum (or difference) also satisfies the wave equation. This principle follows from the fact that every term in the wave equation is linear in the amplitude of the wave.

Consider the sum of two waves y_1(x,t)+y_2(x,t), where y_1(x,t) is the wave described in Part A and y_2(x,t) is the wave described in Part B. These waves have been chosen so that their sum can be written as follows:

y_{\rm s}(x,t) = y_{\rm e}(x) y_{\rm t}(t).

This form is significant because y_e(x), called the envelope, depends only on position, and y_t(t) depends only on time. Traditionally, the time function is taken to be a trigonometric function with unit amplitude; that is, the overall amplitude of the wave is written as part of y_e(x).

Part C  
Find y_e(x) and y_t(t). Keep in mind that y_t(t) should be a trigonometric function of unit amplitude.

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