What Could Be Wrong with My Wave Function Equation?

In summary, the conversation discusses how to write the wave function for a simple, harmonic oscillator generating a wave on a rope. The oscillator operates at a frequency of 40 Hz and with an amplitude of 3.00 cm. The rope has a linear mass density of 50.0 g/m and is stretched with a tension of 4.50 N. The equation for the wave function is y(x,t)=Acos(kx-wt), with A=3, k=8pi, and w=80pi. The conversation also addresses potential issues with calculating the wavelength and making sure the amplitude is in meters.
  • #1
lina29
85
0
A simple, harmonic oscillator at the point x=0 generates a wave on a rope. The oscillator operates at a frequency of 40 Hz and with an amplitude of 3.00 cm. The rope has a linear mass density of 50.0 g/m and is stretched with a tension of 4.50 N.

Write the wave function y(x,t) for the wave moving in +x-direction. Assume that the oscillator has its maximum upward displacement at time t=0.

I know to write the wave function I use the equation y(x,t)=Acos(kx-wt)
where A=3, k=2pi/[tex]\lambda[/tex]=8pi, w=2pif=80pi

So I got the equation y(x,t)=3cos(8pi x-80pi t)

However when I put it in it says the equation is wrong

Can anyone help me in figuring out what I missed?
Thanks
 
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  • #2
How did you calculate the wavelength?
 
  • #3
Make sure the amplitude is in meters, so 0.03 should be the amplitude
 

1. What is the wave function equation?

The wave function equation, also known as the Schrödinger equation, is a mathematical equation that describes how a quantum system, such as an electron, evolves over time. It is a fundamental equation in quantum mechanics and is used to calculate the probability of finding a particle in a certain location.

2. How is the wave function equation used in quantum mechanics?

The wave function equation is used to describe the behavior of quantum particles, such as electrons, in a system. By solving the equation, scientists can determine the probability of finding a particle in a certain location or state. It is also used to calculate the energy levels of particles and to study the behavior of complex systems.

3. What are the components of the wave function equation?

The wave function equation consists of three components: the Hamiltonian operator, the wave function, and the time variable. The Hamiltonian operator represents the total energy of the system, the wave function represents the state of the particle, and the time variable represents the evolution of the particle over time.

4. What is the significance of the wave function equation in understanding the behavior of particles?

The wave function equation is significant because it allows scientists to predict the behavior and properties of particles at the quantum level. It provides a mathematical framework for understanding the probabilistic nature of quantum mechanics and has been instrumental in the development of technologies such as transistors and lasers.

5. How does the wave function equation differ from classical physics equations?

The wave function equation is fundamentally different from classical physics equations because it takes into account the probabilistic nature of quantum particles. Classical equations, such as Newton's laws of motion, describe the behavior of macroscopic objects and are deterministic, meaning they can predict the exact position and momentum of a particle. The wave function equation, on the other hand, only allows for the calculation of probabilities, reflecting the inherent uncertainty at the quantum level.

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