Wave equation - vibration modes

In summary, The conversation discusses a problem sheet with numerical answers and the struggle with question 3 part d. The solution sheet does not include the answer for this part. The previous parts of question 3 have already been completed. The individual requests guidance for part d and shares their attempt to solve it. The answer to part d is the range of angular frequencies being c/a < w < 2c/a.
  • #1
v_pino
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I've attached the problem sheet with the given bottom line numerical answers. I'm struggling with question 3 part d and the solution sheet doesn't include the answer to this part of the question. I've completed the previous parts to question 3 already.

Can someone please guide me through part d? My attempt was to sub in the angular frequency (w) into the given equation c/a < w < 2c/a .

Thank you.
 

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  • #2
Part d: What is the range of angular frequencies for which this waveform is a solution? Answer: The range of angular frequencies for which this waveform is a solution is c/a < w < 2c/a.
 

1. What is the wave equation?

The wave equation is a mathematical formula that describes the behavior of waves. It is a second-order partial differential equation that relates the displacement of a wave to its spatial and temporal coordinates.

2. What are vibration modes?

Vibration modes refer to the different patterns of motion that a system can exhibit when it vibrates. In the context of the wave equation, they describe the different shapes that a wave can take as it propagates through a medium.

3. How is the wave equation used in science?

The wave equation is used in many areas of science, including physics, engineering, and mathematics. It is particularly useful in studying and predicting the behavior of waves in various systems, such as sound waves in air, light waves in optics, and water waves in oceanography.

4. What are the boundary conditions for the wave equation?

The boundary conditions for the wave equation depend on the specific system being studied. In general, they describe the behavior of the wave at the edges of the system, such as the boundaries of a vibrating string or the walls of a container.

5. How is the wave equation derived?

The wave equation is derived from the principles of classical mechanics and the laws of motion, such as Newton's second law. It can also be derived from the more fundamental equations of electromagnetism or quantum mechanics, depending on the specific type of wave being studied.

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