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GATE-2007 (49)

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GATE-2007

Q.49:- A P-wave incident on a horizontal interface between two layers at an angle of 30° generates a reflected S-wave .What is the angle of reflection of the S-wave ?( The P and S-wave velocities in the top layers are 4km/s and 2.5km/s respectively).




Solution:


Formula: using Snells law
  1. \frac{Sin I}{Sin r}=\frac{V1{}}{V2} ( is called the law of refraction for plane seismic waves)


  1. \frac{Sin Ip}{Vp1}=\frac{Sin Is}{Vs1}=\frac{Sin Rp}{Vp2}=\frac{Sin Rs}{Vs2}


Using the second formula \frac{Sin Ip}{Vp1}=\frac{Sin Rs}{Vs2}


Rs is the angle of reflection of the S- wave

Given values are:-


Incident angle of P- wave =30º

Velocities of P-and S waves are


Vp= 4km/s and Vs=2.5 km/s


\frac{Sin 30}{4}=\frac{Sin Rs}{2.5}


\frac{0.5}{4}=\frac{Sin Rs}{2.5}


Sin Rs =\frac{2.5*0.5}{4}


Rs=\arcsin(0.3125)


Rs=18.179


Angle of reflection of a S-wave is =18.179º


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