I must use the wave equation to to find the speed of a wave.

In summary, the conversation is about using the wave equation to find the speed of a wave represented by a position function. The equation for the wave is provided, along with the wave equation and the attempt at a solution. The final answer is determined to be 1.750 m/s using the values for the wave's frequency and wave number. The speaker also mentions having some difficulty with taking derivatives of position functions.
  • #1
afcwestwarrior
457
0

Homework Statement


I must use the wave equation to to find the speed of a wave.

y(x,t) = (3.0mm) sin [(4.00mm^-1)x - (7.00 s^-1)t]




Homework Equations



Here's the wave equation. It has strange symbols.
(∂^2 y) / (∂ x^2) = (1 / v^2) ((∂^2 y)/ (∂^2 t)

The Attempt at a Solution



There's no way that I can attempt this solution if I don't know how to use this formula.
Do I just take the derivative.
 
Last edited:
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  • #2
Nevermind. I figured it out. V = (w/k)

k= 4.00 mm^-1
w = 7.00 s^-1

V= 7/4 = 1.750 m/s
 
  • #3
I don't think your relevant equation is relevant for this problem. You have the equation of the wave for y-position as a function of x-position and time. What do you know about taking derivatives of position functions with respect to time?
 
  • #4
I know how to find Velocity and Acceleration, but when I derive these equations, I have a bit of trouble.
 

What is the wave equation?

The wave equation is a mathematical formula that describes the behavior of a wave. It is typically written as c = λf, where c is the speed of the wave, λ is the wavelength, and f is the frequency.

Why is the wave equation important?

The wave equation is important because it allows us to calculate the speed of a wave using its wavelength and frequency. This is useful in various fields such as physics, engineering, and communication.

How do you use the wave equation to find the speed of a wave?

To use the wave equation, you need to know the wavelength and frequency of the wave. Once you have these values, simply plug them into the equation c = λf and solve for c, which is the speed of the wave.

What are the units of measurement for the wave equation?

The units of measurement for the wave equation depend on the values being used. The speed of the wave (c) is typically measured in meters per second (m/s), the wavelength (λ) is measured in meters (m), and the frequency (f) is measured in hertz (Hz) or cycles per second (s^-1).

Can the wave equation be used for all types of waves?

Yes, the wave equation can be used for all types of waves, including electromagnetic waves, sound waves, water waves, and seismic waves. However, the specific values used for wavelength and frequency may vary depending on the type of wave being analyzed.

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