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sanpokhrel
How can we work out all the properties of wave from differential equation? And what really does differential equation of wave implies?
You don't 'work out' all the properties, exactly; the properties are really what you impose on the conditions. What you do is to write down the Equation of Motion (or the equivalent in electromagnetic terms). This will have second order derivatives (or more) and you can solve it. But you also need to know the boundary conditions and you impose the condition that the solution has the form of a wave (i.e. repeats in space and time). There will be many possible solutions but you choose a simple one for a start - like assuming a sine wave. That doesn't imply that sine waves are the only solution. We know that there are huge possibilities for the shapes of waves.sanpokhrel said:How can we work out all the properties of wave from differential equation? And what really does differential equation of wave implies?
The differential equation of a wave is a mathematical equation that describes the behavior of a wave. It is often written as a function of time and distance, and it includes terms for the wave's amplitude, wavelength, and frequency.
The differential equation of a wave is directly related to the wave's properties. It can be used to determine the wave's speed, amplitude, wavelength, and frequency. By solving the equation, we can understand how these properties change over time and space.
Yes, the differential equation of a wave can be used to predict the behavior of a wave. By solving the equation, we can determine how the wave will evolve over time and space. This is useful in many applications, such as predicting ocean waves or earthquake waves.
While the differential equation of a wave is a powerful tool for understanding wave behavior, it does have some limitations. It assumes that the wave is traveling through a uniform medium and that there are no external forces acting on the wave. In reality, these conditions may not always be met and can affect the accuracy of predictions.
The differential equation of a wave is used in a variety of real-world applications, such as engineering, physics, and geology. It can be used to design structures that can withstand waves, analyze seismic data to understand the Earth's interior, and predict weather patterns based on wave behavior in the atmosphere. It is an essential tool for understanding and studying wave phenomena in many fields.