Which Wave Function Describes a Wave Moving in the -x Direction?

In summary, the conversation is about finding the wave function that describes a wave moving in the -x direction. The three given wave functions are y(x,t) = Asin(-kx-wt), y(x,t) = Asin(kx+wt), and y(x,t) = Acos(kx+wt). The person states that they are unsure about the function y(x,t) = Asin(-kx-wt) and asks for an explanation on how to convert between sine and cosine and adding pi/2. Another person responds by providing a trig identity, sin(-x) = -sin(x), which can help in understanding the movement of the wave.
  • #1
kpx001
15
0

Homework Statement


which of the wave functions describe a wave that moves in the -x direction
y(x,t) =Asin(-kx-wt)
y(x,t)=Asin(kx+wt)
y(x,t)=Acos(kx+wt)


Homework Equations


wave function


The Attempt at a Solution


I know B and C both move left looking at the phase (kx+wt) because its +, however I have no idea about A. I don't know how to convert between sin and cosine or any knowledge of adding pi/2 or anything. can anyone explain this to me? Thank you
 
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  • #2
A trig identity says sin(-x) = - sin(x). This should help.
 
  • #3
.

The wave function y(x,t) describes the displacement of a wave at a given point (x) and time (t). The direction of the wave can be determined by looking at the phase (kx+wt) in the equation. In the first equation, y(x,t) = Asin(-kx-wt), the negative sign in front of kx indicates that the wave is moving in the -x direction. This is because a negative value for kx will result in a negative displacement (y) and therefore the wave is moving in the opposite direction of the positive x-axis.

In the second equation, y(x,t) = Asin(kx+wt), the positive sign in front of kx indicates that the wave is moving in the +x direction. This is because a positive value for kx will result in a positive displacement (y) and therefore the wave is moving in the same direction as the positive x-axis.

In the third equation, y(x,t) = Acos(kx+wt), the positive sign in front of kx also indicates that the wave is moving in the +x direction. This is because a positive value for kx will result in a positive displacement (y) and therefore the wave is moving in the same direction as the positive x-axis.

Therefore, the first equation describes a wave that moves in the -x direction, while the second and third equations describe a wave that moves in the +x direction. The difference between the second and third equations is the starting position of the wave, as the cosine function has a phase shift of pi/2 compared to the sine function. This means that the wave described by the third equation will have a different starting position compared to the wave described by the second equation, but both will still move in the +x direction.
 

1. What is a wave function direction?

A wave function direction refers to the direction in which a wave function, or mathematical representation of a quantum mechanical system, evolves over time. It is typically described in terms of position and momentum.

2. How is wave function direction related to quantum mechanics?

Wave function direction is a fundamental concept in quantum mechanics, as it describes the probabilistic nature of particles at the quantum level. The direction of a wave function determines the probability of finding a particle in a particular position or with a particular momentum.

3. Can wave function direction be observed or measured?

No, wave function direction cannot be directly observed or measured. It is a mathematical concept used to describe the behavior of particles at the quantum level. However, the effects of wave function direction can be observed through experiments and measurements of particle position and momentum.

4. How does wave function direction relate to the uncertainty principle?

Wave function direction is directly related to the uncertainty principle, which states that the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa. This is because wave function direction is a probabilistic concept, and the more precisely we know one variable, the less certain we are about the other.

5. Are there different types of wave function directions?

Yes, there are different types of wave function directions depending on the specific quantum system being studied. For example, in the case of a free particle, the wave function direction will be constant, while in a potential well, the direction may change depending on the position of the particle. Additionally, the direction can also be affected by external forces acting on the particle.

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