Graph of a sinusoidal wave at a fixed position

In summary, the conversation discusses a sound wave described by a given equation and the task of drawing a displacement-versus-time graph for a fixed position. After attempting the graph and receiving feedback, the individual realizes their mistake and successfully creates the correct graph. They also inquire about how to determine the points in between the ones already plotted on the graph.
  • #1
MyNewPony
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Homework Statement



A sound wave is described by D(y,t) = (0.02mm)sin[(8.96 rad/m)y + (3140 rad/s)t + pi/4 rad)], where y is in metres, and t is in seconds.

Draw a displacement-versus-time graph D(y=1.00m,t) at y= 1.00 m from t= 0 s and t= 4 ms.

Homework Equations



D(y,t) = (0.02mm)sin[(8.96 rad/m)y + (3140 rad/s)t + pi/4 rad)]

The Attempt at a Solution



I tried doing the graph (see figure attached), but apparently it's wrong. By 'fixed' position, it means that I must plug in 1.00 m into y for the entire time interval (0 to 4ms), correct? If that's the case, then all the points on the graph should be right. Can someone explain what I'm doing incorrectly?
 

Attachments

  • Sinusoidal Wave.jpg
    Sinusoidal Wave.jpg
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  • #2
Ah, my bad. I jumped the gun and skipped the points in between each tick.
 
  • #3
I got the same graph as you did. How did you figure out how to get the points in between the points you already have on your graph? Because when I plug in y=1 into the equation, I don't get the right answer.
 

What is a sinusoidal wave?

A sinusoidal wave is a type of wave that has a repeating pattern resembling the shape of a sine curve. It is characterized by its amplitude, wavelength, and frequency.

What does the graph of a sinusoidal wave at a fixed position represent?

The graph of a sinusoidal wave at a fixed position represents the displacement of the wave at that particular point in space. It shows how the particles in the medium are moving back and forth as the wave passes through.

How is the amplitude of a sinusoidal wave represented on the graph?

The amplitude of a sinusoidal wave is represented by the height of the wave on the graph. It is measured from the equilibrium position to the highest or lowest point of the wave.

What does the wavelength of a sinusoidal wave represent on the graph?

The wavelength of a sinusoidal wave is represented by the distance between two consecutive peaks or troughs on the graph. It is a measure of the length of one complete cycle of the wave.

How is the frequency of a sinusoidal wave calculated from the graph?

The frequency of a sinusoidal wave can be calculated by dividing the speed of the wave by its wavelength. The speed of the wave can be determined by measuring the distance traveled by the wave in a certain amount of time.

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