Calculating Wave Function for Standing Wave on String

In summary, the conversation is about two traveling waves on a string with a fixed end. The waves have opposite velocities and are identical in amplitude, period, and speed. The resulting standing wave can be represented by the function y(x,t)=(A_sw)(sinkx)(sinwt). The amplitude for the standing wave is 4.92x10^-3m and the angular velocity is 1720rad/s. However, the accuracy of this solution is uncertain due to the lack of information about the wave functions.
  • #1
Scarborm
10
0
Hey!
Here is one that I thought would be easy:

Two traveling waves move on a string that has a fixed end at x=0. They are identical except for opposite velocities. Each has an amplitude of 2.46mm, a period of 3.65ms, and a speed of 111m/s. Write the wave function of the resulting standing wave.

The wave would be represented by the function, y(x,t)=(A_sw)(sinkx)(sinwt)

My answers were: A_sw=2A=4.92x10^-3m
k=w/v=1720/111=15.5/m
w=2*pi/T=2*pi/(3.65x10^-3)=1720rad/s

This is not right though... any ideas? I am least sure about k.
 
Last edited:
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  • #2
What makes you think it isn't right?

If you're not given the actual wave functions,
you can't find the phase in sin(wt+phi)
(so you should leave it as arbitrary).
 
  • #3

Related to Calculating Wave Function for Standing Wave on String

1. What is the wave function for a standing wave on a string?

The wave function for a standing wave on a string is a mathematical representation of the displacement of the string at different points along its length. It is a combination of two traveling waves, one moving to the left and one moving to the right, that interfere with each other to create a stationary pattern.

2. How is the wave function calculated for a standing wave on a string?

The wave function for a standing wave on a string is calculated using the equation y(x,t) = A sin(kx)cos(ωt), where A is the amplitude, k is the wave number, x is the position along the string, and ω is the angular frequency. The wave number and angular frequency can be determined using the properties of the string, such as its tension and mass per unit length.

3. What is the significance of the nodes and antinodes in the wave function for a standing wave on a string?

The nodes and antinodes in the wave function represent the points where the string does not move and moves with maximum amplitude, respectively. These points are important because they determine the wavelength and frequency of the standing wave. The distance between two adjacent nodes or antinodes is half of the wavelength, and the frequency of the wave is determined by how quickly the nodes and antinodes pass a fixed point.

4. Can the wave function for a standing wave on a string be graphed?

Yes, the wave function for a standing wave on a string can be graphed by plotting the displacement of the string (y-axis) against its position along the string (x-axis) at a specific time. This graph will show the characteristic pattern of nodes and antinodes, with the amplitude decreasing towards the nodes and increasing towards the antinodes.

5. How does changing the properties of the string affect the wave function for a standing wave?

Changing the properties of the string, such as its tension or mass per unit length, will affect the wave function for a standing wave. These changes will alter the wave number and angular frequency, resulting in a different wavelength and frequency for the standing wave. As a result, the pattern of nodes and antinodes will also change, and the amplitude and displacement of the string at different points will be affected.

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