Question

An earthquake P wave traveling at 7.7km/s strikes a boundary within the Earth between two kinds of material.If it approaches the boundary at an incident angle of 44? and the angle of refraction is 33?, what is the speed in the second medium?Express your answer to two significant figures and include the appropriate units.

Answer 1

Answer:

$c_2 = 6.04\ Km/s$

Explanation:

given,

speed of wave, c₁ = 7.7 m/s

angle of incidence, i = 44°

angle of refraction, r = 33°

speed of wave in second medium.

using Snell's law

  n₁ sin i = n₂ sin r

$\dfrac{n_1}{n_2}=\dfrac{sin\ r}{sin\ i}$

$\dfrac{n_1}{n_2}=\dfrac{sin\ 33^0}{sin\ 44^0}$

$\dfrac{n_1}{n_2}=0.784$

now,

calculation of velocity in the medium

n₁ c₁ = n₂ c₂

$\dfrac{n_1}{n_2}=\dfrac{c_2}{c_1}$

$c_2 = c_1\times \dfrac{n_1}{n_2}$

$c_2 = 7.7\times 0.784$

$c_2 = 6.04\ Km/s$

Speed of wave in the second medium is equal to 6.04 Km/h