Looking for speed using the wave equation

In summary, the conversation discusses the equation phi(x,t) = A e *[-a(bx+ct)*2] and the attempt to find its speed. The equation is in the negative x-direction and has a constant a, amplitude A, and speed of light c. The individual is trying to solve for the speed using the formula V=W/K or V=B/A, but is having difficulty due to not having any numbers besides c. They are also considering using partial fractions, but are not allowed to do so. They also mention that any function f(x + vt) is a wave traveling in the -x direction with speed v.
  • #1
Ashley1nOnly
132
3

Homework Statement


phi(x,t) = A e *[-a(bx+ct)*2]
I'm trying to find the speed of the equation

Homework Equations


f(x+vt) +vt which means it is in the negative x-direction
f(x)= e^-ax^2
plugging in x'=x+vt
A e *[-a(bx+ct)*2]
where a= constant A= amplitude v=c= speed of light

The Attempt at a Solution


I know that is speed = w(angular frequency)/K
This issue that I am having is that I don't have any number besides c which is the speed of light
I know that I can use partial fractions [partial phi/ partial t]divided by [partial phi/ partial x] but I'm not allowed to use that way. What is another way I can solve this problem
 
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  • #2
V=W/K
V=B/A
SINCE IT IS GOING IN THE -X DIRECTION
 
Last edited:
  • #3
ANY function f(x + vt) is a wave traveling in the -x direction with speed v.
Consider: at t=x=0 the function is max = A. For t>0 what values of x maintain the value f=A?
 

Related to Looking for speed using the wave equation

1. What is the wave equation and how is it used to measure speed?

The wave equation is a mathematical formula that describes the behavior of waves. It is used to calculate the speed of a wave by taking into account the wavelength and frequency of the wave. The equation is v = λf, where v is the speed of the wave, λ is the wavelength, and f is the frequency.

2. How does the wave equation apply to different types of waves?

The wave equation applies to all types of waves, including electromagnetic waves, sound waves, and water waves. It is a universal formula that can be used to calculate the speed of any type of wave as long as the wavelength and frequency are known.

3. Can the wave equation be used for waves in different mediums?

Yes, the wave equation can be used for waves in different mediums. However, the speed of the wave may vary depending on the properties of the medium, such as its density and elasticity. The wave equation takes these factors into account and can be adjusted to calculate the speed in different mediums.

4. Is the wave equation affected by external factors?

The wave equation is not affected by external factors such as temperature, pressure, or gravity. These factors may affect the properties of the medium through which the wave is traveling, but they do not directly impact the speed of the wave calculated using the wave equation.

5. How accurate is the wave equation in measuring speed?

The wave equation is a highly accurate method for calculating the speed of a wave. However, there may be slight variations in the calculated speed due to factors such as the precision of the measured wavelength and frequency, and any potential errors in the equation itself. Overall, the wave equation provides a reliable and precise measurement of wave speed.

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