Stress/strain, Hooke’s lawEAS-450 – Physics and Chemistry of the EarthLab exercise – Seismic wave propagationObjective: Understand strain and stress in elastic solids. Manipulate the propagation of seismic waves. Locate an earthquake.Stress/strain, Hooke’s law1. A 4.00 m long steel wire has a diameter of 1.50 mm. A 500 N tensile force is applied and it stretches 5.40mm. Calculate:a. The strain of the wire;b. The stress applied to the wire;c. The Young's modulus of this steel.Propagation of seismic waves2. The following equation describes the propagation of a seismic wave (cf. lecture notes):TtxAy2sin[x = distance along x-axis (m), y = distance along y-axis (m), t = time (s), A = amplitude (m), T = period (s),  = wavelength (m)]Since the velocity is the distance traveled by the wave in 1 second, on can write that: velocity= frequency x wavelength, or:  fV ( = wavelength, f = frequency).a. For a wavelength, of = 6 km, an amplitude of 10 mm, and a wave velocity of v= 5 km/s, use the equations above to draw the wave (i.e., plot y versus x) over the interval between x = -3 km and x = 3 km at time t = 0 s. What is the amplitude of the wave?b. For the same wavelength, velocity, and interval, draw the wave at time t = 0.2 s.3. A rock has its rigidity modulus equal to ¾ of its bulk modulus. If melting the rock does not change its bulk modulus or density, what will be the ratio of Vp in the solid to that in the liquid?4. Suppose that an earthquake at a distance of 200 km due south of Purdue University occurs at 01:00 AM. Assuming typical velocities for P waves (v = 6 km/s) and S waves (v = 3.5 km/s) and a perfectly elastic propagation medium:a. At what time will the P wave arrive at Purdue? (first write the equation that gives the arrival time as a function of the origin time, of the epicentral deistance, and of the wave velocity, then calculate the numerical value)b. At what time will the S wave arrive at Purdue? (same as above)c. Same questions as a. and b. with a 50 km distance between the earthquake and Purdue.d. Derive the equation that gives the difference of arrival time between P and S waves as a function of the distance between the earthquake and the seismic station.e. Using this equation, can you imagine a simple way to locate an earthquake?5. On February 18, 1996 at 01:45 UT an earthquake occurred in France. It was recorded by 3 seismic stations. a. Using the seismograms below, measure the difference of arrival time between P and S waves at each station.b. Use your S-P reading to calculate the epicentral distance to each stationc. Locate the earthquake graphically (map, ruler, and compass!)d. What are the main factors that limit the accuracy of your location determination?Station name Latitude Longitude S-P (seconds)Epicentral distance (km)EPF 42o30”00.0”N 00o24’00.0”EVIV 44o51’22.0”N 04o40’22.0”ELFF 44o56’22.3”N 00o44’24.6”EHint: Get help from http://www.sciencecourseware.com/eec/Earthquake/, a great site to learn about earthquakes!x-axis: time in secondsy-axis: velocity in