# Check 2 waave displacement equations please

• Lengalicious
In summary, when two harmonic oscillators superpose, the total displacement is the sum of the two displacements. If you wish you can try to simplify or otherwise put the expression into a different form that shows something interesting.
Lengalicious
Got to calculate the superposition of a couple o' waves, wanted to double check if they are both the same frequency and wavenumber?x1(t) = 3 sin(2t + /4 ) and x2(t) = 3 cos(2t).

I take it 2 is the frequency? And since Kx is not inside the function how can I know whether the wave numbers the same? :S

These are not waves. The equations have to spatial variable. They may represent two harmonic oscillations with a phase difference of pi/4.
2∏ is the angular frequency, ω=2∏f. The frequency is 1 Hz.

Ok thanks, when 2 harmonic oscillators superpose do you just take the sum of the two even though they have different phases?
EDIT: Since one is in terms of sin and the other in cos, do i make sin(2pit+pi/4) into cos(2pit+pi/4+pi/2) or is that not valid, because i need to use the trig sum-product identity

Last edited:
Yes, you add the functions. You don't need a trig sum-product identity. Use the phase identity sin(x) = cos(x-pi/2)

Lengalicious said:
Ok thanks, when 2 harmonic oscillators superpose do you just take the sum of the two even though they have different phases?
EDIT: Since one is in terms of sin and the other in cos, do i make sin(2pit+pi/4) into cos(2pit+pi/4+pi/2) or is that not valid, because i need to use the trig sum-product identity
Depends what you mean by the "take the sum".
At any time, the total displacement is the sum of the two displacements (superposition principle):
x(t)=x1(t)+x2(t)
If you wish you can try to simplify or otherwise put the expression into a different form that shows something interesting.
You cannot use the trig identity as the two have difefrent amplitudes.
For the given case, you can write the result as a single cosine or sine,
x(t)=Asin(2∏t+ψ).
To find the values of A and ψ you can expand the sin and and identify the terms with the original components. You'll find two equations in the variables A and ψ.
Phasor algebra is a more straightforward method, if you are familiar with it.

## 1. What are the two wave displacement equations?

The two wave displacement equations are the displacement equation for a transverse wave and the displacement equation for a longitudinal wave. The transverse wave displacement equation is y(x,t) = A sin(kx - ωt), and the longitudinal wave displacement equation is y(x,t) = A sin(kx - ωt).

## 2. How do you calculate the wave displacement?

The wave displacement can be calculated by using the wave displacement equations, which take into account the amplitude (A), wave number (k), angular frequency (ω), position (x), and time (t).

## 3. What do A, k, and ω represent in the wave displacement equations?

A represents the amplitude, which is the maximum displacement of the wave from its equilibrium position. k represents the wave number, which is the number of waves per unit distance. ω represents the angular frequency, which is the rate at which the wave oscillates.

## 4. How do the wave displacement equations differ for transverse and longitudinal waves?

The displacement equations for transverse and longitudinal waves differ in the direction of the wave motion. In a transverse wave, the displacement is perpendicular to the direction of the wave, while in a longitudinal wave, the displacement is parallel to the direction of the wave.

## 5. Can the wave displacement equations be used for all types of waves?

Yes, the wave displacement equations can be used for all types of waves, including electromagnetic, mechanical, and even water waves. However, the specific values for A, k, and ω may differ depending on the type of wave.

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