Wave function at origin on transverse wave

In summary, the wave function at the origin, given by the simple harmonic equation for a transverse wave, is y(0,t)=Acos(10∏t). This means that when x = 0 and t varies, the wave function is equal to Acos(10∏t). It is important to confirm with your teacher or clarify the meaning of "at the origin" in order to correctly interpret and solve the problem.
  • #1
Saxby
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Homework Statement


You have the simple harmonic equation for a transverse wave which is y(x,t)=Acos(10∏t+5x), what is the wave function at the origin

The Attempt at a Solution


By "at the origin" does it mean where x=0 and t=0. Because it that case y=Acos0 and therefore y=A. Is that right?
 
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  • #2
I would interpret it to mean to let x = 0 and let t vary, but your interpretation may also be what was meant.
 
  • #3
I am sure the question wants you take it as when x = 0 and t various
so y(0,t)=Acos(10∏t) = wave function at origin.
 
  • #4
Thanks guys, I talked to my teacher and i can safely conclude the answer is y(0,t)=Acos(10∏t)
 
  • #5


Yes, that is correct. At the origin, where x=0 and t=0, the wave function is simply y=A, which represents the amplitude of the wave at that point in time. This is because the cosine function of 0 is equal to 1, and multiplying it by the amplitude A gives the value of A.
 

FAQ: Wave function at origin on transverse wave

1. What is a wave function at origin on a transverse wave?

A wave function at origin on a transverse wave is a mathematical representation of the displacement of a transverse wave at a specific point in space and time. It describes the amplitude and direction of the wave's oscillations at the origin point.

2. How is a wave function at origin different from other wave functions?

A wave function at origin is specific to transverse waves, which are waves that oscillate perpendicular to the direction of propagation. Other wave functions, such as those for longitudinal waves, describe the displacement of the wave parallel to its direction of propagation.

3. What is the significance of the wave function at origin on a transverse wave?

The wave function at origin is important because it allows us to understand the characteristics of a transverse wave at a specific point. By analyzing the wave function, we can determine the amplitude, wavelength, and frequency of the wave at the origin point, which provides valuable information for studying and predicting wave behavior.

4. How is the wave function at origin calculated?

The wave function at origin is typically calculated using mathematical equations that describe the motion of transverse waves, such as the sine or cosine function. These equations take into account the amplitude, wavelength, and frequency of the wave, as well as the position and time at the origin point.

5. Can the wave function at origin change over time?

Yes, the wave function at origin can change over time as the transverse wave propagates through space. This is because the amplitude, wavelength, and frequency of the wave may change as it interacts with different mediums or obstacles. However, the mathematical equations used to calculate the wave function remain the same, so the changes can be predicted and understood.

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