Cross section of a S wave

However, there may be other methods to derive the same result. In summary, the total cross section of a S wave can be calculated using the equation Sigma=(pi/k)*(b^2)/((E-En)^2+(b/2)^2)). By setting E=En, the maximum value of Sigma is obtained, and by halving this value and solving for E, we get two solutions (E1 and E2) that are separated by a distance of b. This shows that b is the width of the resonance. Although the calculation can be done using basic math, there may be other methods that involve more physics.
  • #1
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Homework Statement


The total cross section of a S wave is given by the following equation
Sigma=(pi/k)*(b^2)/((E-En)^2+(b/2)^2))
prove that b is the width of the resonance.


Homework Equations


Nothing that is the only thing


The Attempt at a Solution


I already solved the question using basic calculation.
For E=En i get the maximum of Sigma , for half of that maximum , i get a second degree equation of E, when solving it i get 2 solution representing that half maximum(E1 & E2) , the difference between E1 and E2 , E1-E2=b
But I'm not really comfortable with the way i did it , I know i got the solution , but I'm looking for another way , something more to do with physics.
idea anyone?
 
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  • #2
You did it correctly. Somtimes physics depends on simple math.
 

1. What is a cross section of a S wave?

A cross section of a S wave is a representation of the horizontal slice of the Earth's interior that intersects with the path of an S wave. It shows the amplitude and direction of particle motion of the wave as it travels through the Earth.

2. How is a cross section of a S wave different from a P wave?

A cross section of a S wave differs from a P wave in terms of particle motion. S waves have transverse motion, meaning the particles move perpendicular to the direction of wave propagation, while P waves have longitudinal motion, with particles moving parallel to the direction of wave propagation.

3. How does a cross section of a S wave provide information about the Earth's interior?

A cross section of a S wave provides information about the Earth's interior by showing the different layers and structures that the wave passes through. The changes in amplitude and direction of particle motion can indicate the density and composition of the material the wave encounters.

4. What do the different colors represent in a cross section of a S wave?

The different colors in a cross section of a S wave represent the amplitude or strength of the wave at different points along the cross section. Typically, warmer colors such as red and orange indicate higher amplitudes, while cooler colors like blue and green represent lower amplitudes.

5. How are cross sections of S waves used in earthquake studies?

Cross sections of S waves are used in earthquake studies to help determine the location, magnitude, and focal mechanism of earthquakes. By analyzing the amplitude and direction of particle motion on multiple cross sections, seismologists can gain a better understanding of the earthquake's source and the structure of the Earth's interior in that region.

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