Wave Consine Equation: Reflection & Transmission

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In summary, the wave cosine equation is a universal mathematical formula that describes the behavior of waves as they reflect and transmit through different mediums. It is commonly used in physics and engineering to calculate the reflection coefficient and is applicable to all types of waves. Factors such as the angle of incidence, medium properties, and frequency can affect the reflection and transmission of a wave, making the wave cosine equation a valuable tool in various industries.
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mcheung4
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This is about wave reflection and transmission.

For an infinite string with a density change at x=0, consider an incident wave propagating to the right from x = -∞. The most general form is W = A cos(w(t-x/c)+θ), with amplitude A, angular freuqency w, time t, distance x (from origin), wave speed c and phase θ.

I do not understand the term (t-x/c). Shouldn't it be just t since we're starting from infinity? Thanks!
 
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  • #2
To me it looks like: t=time at your location, -x/c=time required to get from x to the origin at speed c.
 

Related to Wave Consine Equation: Reflection & Transmission

1. What is the wave cosine equation?

The wave cosine equation is a mathematical formula that describes the behavior of a wave as it reflects and transmits through a medium. It is commonly used in physics and engineering to understand the properties of waves.

2. How is the wave cosine equation used to calculate reflection?

The wave cosine equation can be used to calculate the reflection coefficient, which is a measure of how much of a wave is reflected when it encounters a change in medium. This is done by comparing the amplitude of the incident wave to the amplitude of the reflected wave.

3. Can the wave cosine equation be applied to all types of waves?

Yes, the wave cosine equation can be applied to all types of waves, including electromagnetic waves, sound waves, and water waves. It is a universal equation that describes the behavior of waves regardless of their frequency or medium.

4. What factors affect the reflection and transmission of a wave?

The reflection and transmission of a wave are affected by several factors, including the angle of incidence, the properties of the medium it is traveling through, and the frequency of the wave. These factors can change the behavior of the wave and alter the values calculated by the wave cosine equation.

5. How is the wave cosine equation used in real-world applications?

The wave cosine equation has many practical applications, such as in the design of antennas, mirrors, and lenses. It is also used in industries such as telecommunications, acoustics, and oceanography to understand and predict the behavior of waves in different scenarios.

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