Determining Parameters of a Transverse Harmonic Wave

In summary, the profile of a transverse harmonic wave with a velocity of 1.2 m/s can be described by the equation y(x)=(0.02 m)sin[157 rad m^-1)x]. To determine the amplitude, wavelength, frequency, angular frequency, and period of this wave, we can use the equations A = 0.02 m, λ = 2π/k, v = λƒ, ω = 2πƒ. By plugging in the given values for velocity and the equation for k, we can solve for the other quantities. The amplitude is 0.02 m, the wavelength is approximately 0.04 m, the frequency is approximately 78.5 Hz,
  • #1
ashlieketchum
1. “The profile of a transverse harmonic wave, traveling at 1.2 m s^-1 is given by y(x)=(0.02 m)sin[157 rad m^-1)x]. Determine amplitude, wavelength, frequency, angular frequency, and period.

Homework Equations



y(x,t)=Acos(kx-wt)[/B]

The Attempt at a Solution


I attempted to change it to a cosine function but I’m still left with a position equation as opposed to a displacement equation. I’m not sure what steps to take to get the equation into the form above.
 
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  • #2
ashlieketchum said:
... I’m still left with a position equation as opposed to a displacement equation.
I am not sure what you mean by this. You are given an equation containing numbers. How are these numbers related to the quantities you are looking for? Look at the relevant equation you posted and figure it out. For example, what does the symbol A stand for? And so on and so forth.
 
  • #3
you don't have to turn this equation to this form y(x,t)=Acos(kx-wt) !

all the answers you already have in this :
V = 1.2 m s^-1
y(x)=(0.02 m)sin[157 rad m^-1)x]

hints :

y(x) = A sin(Kx) ... K = 2π / λ
V = λƒ
ω = 2πƒ
 
  • #4
patric44 said:
you don't have to turn this equation to this form y(x,t)=Acos(kx-wt) !
Not really. You can answer what is asked from what is given without putting in the time dependence. To say it differently, you are given y(x,0) = Acos(kx-0) so it is in this form but at the specific instant t = 0. All you have to do is figure out which number is k, which is A and how to get the rest of the quantities.
 

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The "Optics wave function problem" is a theoretical issue in optics that arises when trying to describe the behavior of light using a wave function. It is a fundamental problem in quantum mechanics, as it highlights the difficulty of reconciling classical wave theories with the quantized behavior of light particles.

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