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Shown in the figure in the vertical plane and

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shown in the figure) in the vertical plane and parallel to the direction of propagation. Amplitude decreases with depth. Material returns to its original shape after the wave passes.
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Review: Exciting a wave, longitudinal and transverse waves (a) Pushing at the spring’s end with a force over a distance (work) cause the A-B coils to add elastic (compressional) energy. This energy then propagates to the right. (b) The end of the spring is pulled back with a force over a distance (work) to add elastic (dilitational) energy. Note relation between propagation direction and wave vibration direction. (a) Longitudinal P-wave (b) Transverse S-wave
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Concept: a wave pulse versus a sinusoidal wave Two ‘kinds’ of waves: A harmonic sinusoidal wave F(x,t) = A*sin( x– t) that oscillates up and down across all space and time (everywhere!). A is wave amplitude. A space-time localized wave pulse that is a superposition of many different frequency components moving in unison (phase).
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Relation between wave raypaths and wavefronts An explosion makes a force that creates a wave pulse that propagates outwards in time. The increasing diameter circles are the wave-fronts at successively increasing times. Draw the rays. Rays are a very useful concept that shows the path that one parcel of the wavefront travels along. Each ray is always perpendicular to the wavefront. The ray has an arrow to indicate the direction of energy transport.
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Measuring very small motions at the Earth’s surface in 3- dimensions The ground motion (displacement, velocity, acceleration) at the surface is measured by seismometers . Because space is three-dimensional, we will need to record the ground motion in three perpendicular directions ( up-down, north-south, east-west ). A seismometer works by hanging a mass that is from a frame attached firmly to the earth so that the frame moves with the ground motion. The trick to an inertial seismometer is that the inertia of the mass suspended by the spring causes the mass to ‘lag behind’ the motion of the frame. This cause the mass to be displaced with respect to the frame, and this displacement can be measured by the ‘ruler’. In modern system the motion is amplified a million times.
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A modern seismometer: an inertial magnet inside a coil As before, a mass (inertia) is hanging from a spring attached the frame (case) of the seismometer attached to the earth. As the inertial mass ‘lags’ behind the motion of the case, there is differential motion between the mass and the electrical coil that can be measured via electrical induction. The trick is that the mass is magnetized vertically (note poles). So as the magnet (mass) moves with respect to the coil, a current is induced in the coil circuit that can be measured at the two wires. The voltage associated with the current will be proportional to the velocity of the ground motion!
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Spherical symmetry of the Earth In a spherical geometry , the distance between two points on the earth’s surface is denoted by the angle subtended from the center of the earth. This is called the
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