What is the Velocity of a Wave Pulse Described by y(x,t)=De^-(Bx-Ct)^2?

In summary, the speed of a wave pulse is the rate at which a disturbance travels through a medium, and it can be calculated by dividing the distance traveled by the time taken or by multiplying the frequency and wavelength. It depends on the properties of the medium it travels through, such as density, elasticity, and temperature, and is directly proportional to frequency and inversely proportional to wavelength. The speed can also change if the medium or its properties change.
  • #1
rizardon
20
0

Homework Statement


A wave pulse is described by the function y(x,t)=De^-(Bx-Ct)^2, where B, C and D are all positive constants. What is the speed of this wave?


Homework Equations


y=f(x+vt)


The Attempt at a Solution


y=De^-(Bx-Ct)^2 is of the form y=f(x+vt)
however there is a B in front of x so I factor the B out and get
-(Bx-Ct)^2 = -B^2(x-Ct/B)^2
so the velocity is C/B
Is this the right approach?
 
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  • #2
yes.
 

Related to What is the Velocity of a Wave Pulse Described by y(x,t)=De^-(Bx-Ct)^2?

1. What is the speed of a wave pulse?

The speed of a wave pulse is the rate at which the disturbance travels through a medium. It is a measure of how fast the energy of the wave is transferred from one point to another.

2. How is the speed of a wave pulse calculated?

The speed of a wave pulse can be calculated by dividing the distance the wave travels by the time it takes to travel that distance. It can also be calculated by multiplying the frequency of the wave by its wavelength.

3. Does the speed of a wave pulse depend on the medium it travels through?

Yes, the speed of a wave pulse depends on the properties of the medium it travels through, such as density, elasticity, and temperature. Different mediums can have different speeds of propagation for the same type of wave.

4. How does the speed of a wave pulse relate to its frequency and wavelength?

The speed of a wave pulse is directly proportional to its frequency and inversely proportional to its wavelength. This means that as the frequency increases, the speed of the wave also increases, and as the wavelength increases, the speed of the wave decreases.

5. Can the speed of a wave pulse change?

Yes, the speed of a wave pulse can change if the medium it travels through changes. For example, the speed of sound waves in air is different from the speed of sound waves in water. Additionally, the speed of a wave pulse can also change if the properties of the medium, such as temperature or pressure, change.

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