# Finding the equation of a wave. ?Easy?

• Patdon10
In summary, we are given a wave traveling at 34 m/s in the positive x-direction with a frequency of 49 Hz. The function for the wave is written as y(x, t) = A*sin(kx + wt + phi), where x and y are in meters and t is in seconds. Additionally, at x = 0 and t = 0, the wave has a velocity of 2.3 m/s and a vertical displacement of 5 mm. To solve this problem, we must consider the relationship between position and velocity and use it to find the necessary values for the wave function.
Patdon10

## Homework Statement

A wave travels along a string in the positive x-direction at 34 m/s. The frequency of the wave is 49 Hz. At x = 0 and t = 0, the wave velocity is 2.3 m/s and the vertical displacement is y = 5 mm. Write the function
y(x, t)
for the wave. (Use the following as necessary: x and t. Assume x and y are in m, and that t is in s.)

## Homework Equations

sinusoidal wave:
y = Asin(kx+wt+phi)

## The Attempt at a Solution

I'm trying to understand all of this. I really don't though. I believe the y displacement has something to do with amplitude, correct? Why is there 2 different wave velocities?
If anyone could give me a nudge in the right direction, I'd really appreciate it.

\begin{align} v &= 34 m/s \\ f &= 49 Hz \\ y(0, 0) &= 5 mm \\ y(x, t) &= A\sin{kx + \omega t + \phi} \end{align}

However, this just gives us the displacement of the wave in the y-direction as a function of position in the x-direction and time. There is additional information given, and that has to deal with velocities. What's the relationship between position and velocity, and how can we use that relationship to help solve this problem?

## 1. What is the equation of a wave?

The equation of a wave is a mathematical representation of the relationship between the physical properties of a wave, such as its amplitude and wavelength, and its motion through space and time.

## 2. How can I find the equation of a wave?

The equation of a wave can be found by using the wave equation, which is given by: y = A sin(kx - ωt) where y is the displacement of the wave, A is the amplitude, k is the wave number, x is the position, ω is the angular frequency, and t is the time.

## 3. What is the wave number in the wave equation?

The wave number, represented by k, is a constant that is related to the wavelength of the wave. It is defined as the number of wave cycles that pass through a given point in one unit of time.

## 4. Is finding the equation of a wave easy?

The complexity of finding the equation of a wave depends on the type of wave and the information available. In simple cases, such as a basic sinusoidal wave, it can be relatively easy. However, for more complex waves, it may require advanced mathematical techniques and data analysis.

## 5. What are the applications of the wave equation?

The wave equation has a wide range of applications in various fields such as physics, engineering, and mathematics. It is used to describe and analyze different types of waves, including sound waves, electromagnetic waves, and water waves. It is also used in the study of wave propagation, wave interference, and wave phenomena.

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