Find the Speed and Direction of a Wave with Constants A, B, and C

In summary, the wave described by the equation y(x,t)=Ae^{Bx^2+BC^2t^2-2BCxt} has a speed of C in the positive x direction, with constants A, B, and C. However, it is missing an imaginary constant in the exponential, which is necessary for the wave equation to be satisfied.
  • #1
azatkgz
186
0

Homework Statement


What's the speed and direction of the following wave(A,B and C are constants)
[tex]y(x,t)=Ae^{Bx^2+BC^2t^2-2BCxt}[/tex]


The Attempt at a Solution


[tex]y(x,t)=Ae^{B(x-Ct)^2}[/tex]

from (x-Ct)

v=C in the +x direction
 
Physics news on Phys.org
  • #2
Are you missing the imaginary constant in your exponential? If so, then you are correct. If not, you have a diverging or decaying exponential rather than a plane wave.
 
  • #3
No,it's original question.There's no imaginary constant.
So my solution is true.Thanks for checking.
 
  • #4
No, there has to be an imaginary constant. You need to have something of the form

[tex]Ae^{i(x-vt)}[/tex]

Regular exponentials don't satisfy the wave equation. The wave equation says that two derivatives in time equal two derivatives in space divided by the velocity squared.
 

FAQ: Find the Speed and Direction of a Wave with Constants A, B, and C

What is the formula for finding the speed of a wave with constants A, B, and C?

The formula for finding the speed of a wave with constants A, B, and C is: speed = A x B / C. This formula is known as the wave speed equation and is commonly used in physics and engineering.

What do the constants A, B, and C represent in the wave speed equation?

Constants A, B, and C represent different properties of the wave. A represents the amplitude of the wave, B represents the wavelength, and C represents the period of the wave.

Can the wave speed equation be used for all types of waves?

Yes, the wave speed equation can be used for all types of waves, including sound waves, light waves, and water waves. However, the values of constants A, B, and C may vary depending on the type of wave.

How can I measure the constants A, B, and C in order to find the wave speed?

The constants A, B, and C can be measured using different methods depending on the type of wave. For example, the amplitude can be measured using a ruler, the wavelength can be measured using a measuring tape or ruler, and the period can be measured using a stopwatch.

What units should be used for the constants A, B, and C in the wave speed equation?

The units used for constants A, B, and C in the wave speed equation will depend on the units used to measure the amplitude, wavelength, and period of the wave. It is important to use the same units for all three constants in order to get an accurate calculation of the wave speed.

Similar threads

Replies
9
Views
341
Replies
5
Views
354
Replies
2
Views
1K
Replies
13
Views
1K
Replies
3
Views
1K
Replies
10
Views
1K
Back
Top