Writing an equation for a wave

In summary, the conversation discusses the process of writing an equation for a wave with specific parameters, including amplitude, wave vector, angular frequency, and time. The general equation for waves is y = A sin (wt ± kx), where A represents amplitude, w represents angular frequency, t represents time, and k represents wave vector. The conversation also mentions the importance of ensuring the argument of the Sine function is dimensionless and the potential mistake of using the wrong time component in the equation.
  • #1
rugapark
22
0
I needed to write an equation for a wave with:

amplitude : 2cm
wave vector : 502.7
angular frequency : 125.7 Hz
time : 0 sec

and I used the general equation for waves to come up with:

y = 0.02 sin (125.7 - 502.7x)

is that alright?
 
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  • #2
What is the general equation you used (and what do the constants mean)?

Also, what do you mean by: wave vector = some number ?
 
  • #3
y=A sin (wt[tex]\pm[/tex]kx) is the formula where

A = amplitude
w = angular freq.
t = time
k = wave vector

wave vector doesn't have units as it's a vector quantity.. right?
 
  • #4
rugapark said:
wave vector doesn't have units as it's a vector quantity.. right?

You might want to reconsider this statement. Displacement is a vector quantity, would you agree that displacement has a unit?

One hint - the argument of the Sine function must be dimensionless.

I agree with your general equation. However, using the conditions you gave (t=0) are you sure that you're happy with the time component of the argument? Remember your multiplying the angular velocity and time, with the time equal to zero. Are you sure this would give you the angular velocity back, like your expression suggests?

Kind Regards

Barny
 
  • #5
What's given for frequency is Hz, usually represented by f. The radian frequency, w, is w=2*pi*f. However, the wave equation has w*t. If t is zero, then that product is zero, and there is no need to convert.
 

1. What is the equation for a wave?

The general equation for a wave is given by y = A sin (kx - ωt + φ), where y is the displacement of the wave, A is the amplitude, k is the wave number, ω is the angular frequency, x is the position, t is the time, and φ is the phase shift.

2. How do you determine the amplitude of a wave?

The amplitude of a wave is the maximum displacement of the wave from its equilibrium position. It can be determined by measuring the height of the wave from the equilibrium position to the crest (highest point) or trough (lowest point) of the wave.

3. What does the wave number represent in the wave equation?

The wave number (k) represents the number of complete wave cycles per unit distance, usually measured in radians per meter. It is related to the wavelength (λ) of the wave by the equation k = 2π/λ.

4. How does the angular frequency affect the wave?

The angular frequency (ω) determines the speed at which the wave propagates in a medium. It is directly proportional to the frequency (f) of the wave, which is the number of wave cycles per unit time. The relation between angular frequency and frequency is given by ω = 2πf.

5. What does the phase shift represent in the wave equation?

The phase shift (φ) represents the position of the wave relative to a fixed point in time and space. It is usually measured in radians and can have values ranging from 0 to 2π. A phase shift of 0 indicates that the wave is in phase with the fixed point, while a phase shift of π indicates that the wave is 180 degrees out of phase.

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