Monday, May 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu1PHYS 1441 – Section 004Lecture #24Monday, May 3, 2004Dr. Jaehoon Yu•Waves• Speed of Waves• Types of Waves• Energy transported by waves• Reflection and Transmission• Superposition principleFinal Exam Next Monday, May. 10!Monday, May 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu2Announcements• Quiz results– Average score: 47.9/100• Other quizzes: 38.2, 41, 57.9 and 52.4– Top score: 90• Final exam Monday, May 10– Time: 11:00am – 12:30pm in SH101– Chapter 8 – 11– Mixture of multiple choices and numeric problems– Pick up your exercise problems• Review this Wednesday, May 5.Monday, May 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu3Wave MotionsWaves do not move medium rather carry energy from one place to anotherTwo forms of waves–Pulse– Continuous or periodic waveMechanical WavesMonday, May 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu4Characterization of Waves• Waves can be characterized by– Amplitude: Maximum height of a crest or the depth of a trough– Wave length: Distance between two successive crests or any two identical points on the wave– Period: The time elapsed by two successive crests passing by the same point in space.– Frequency: Number of crests that pass the same point in space in a unit time • Wave velocity: The velocity at which any part of the wave movesvTλ=fλ=Monday, May 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu5Waves vs Particle VelocityIs the velocity of a wave moving along a cord the same as the velocity of a particle of the cord? No. The two velocities are different both in magnitude and direction. The wave on the rope moves to the right but each piece of the rope only vibrates up and down.Monday, May 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu6Speed of Transverse Waves on StringsHow do we determine the speed of a transverse pulse traveling on a string?If a string under tension is pulled sideways and released, the tension is responsible for accelerating a particular segment of the string back to the equilibrium position.The speed of the wave increases.So what happens when the tension increases? Which law does this hypothesis based on?Based on the hypothesis we have laid out above, we can construct a hypothetical formula for the speed of wave For the given tension, acceleration decreases, so the wave speed decreases.Newton’s second law of motionThe acceleration of the particular segment increases µTv =Which means? Now what happens when the mass per unit length of the string increases? T: Tension on the stringµ: Unit mass per lengthIs the above expression dimensionally sound?T=kg m/s2. µ=kg/m(T/µ)1/2=[m2/s2]1/2=m/sTmL=Monday, May 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu7Example 11 – 10Wave on a wire. A wave whose wavelength is 0.30m is traveling down a d 300-m long wire whose total mass is 15 kg. If the wire is under a tension of 1000N, what is the velocity and frequency of the wave? The speed of the wave isvTµ=1000140 /15/300ms==The frequency of the wave isfvλ=140 /4700.30msHzm==Monday, May 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu8Example for Traveling WaveA uniform cord has a mass of 0.300kg and a length of 6.00m. The cord passes over a pulley and supports a 2.00kg object. Find the speed of a pulse traveling along this cord.Thus the speed of the wave isSince the speed of wave on a string with line density µ and under the tension T is TM=2.00kg1.00m5.00mµTv =The line density µ ismkgmkg/1000.500.6300.02−×==µThe tension on the string is provided by the weight of the object. ThereforevTµ=219.619.8 /5.00 10ms−==×Mg=22.00 9.80 19.6 /kg m s=×= ⋅Monday, May 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu9Type of Waves• Two types of waves– Transverse Wave : A wave whose media particles move perpendicular to the direction of the wave– Longitudinal wave: A wave whose media particles move along the direction of the wave• Speed of a longitudinal waveElastic Force Factorinertia factorv =Evρ=For solidE:Young’s modulusρ: density of solidBvρ=liquid/gasE: Bulk Modulusρ: densityMonday, May 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu10Example 11 – 11Sound velocity in a steel rail. You can often hear a distant train approaching by putting your ear to the track. How long does it take for the wave to travel down the steel track if the train is 1.0km away? The speed of the wave isvEρ=The time it takes for the wave to travel istlv=331.0 100.205.1 10 /msms×==×11 23332.0 10 /5.1 10 /7.8 10 /Nmmskg m×==××Monday, May 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu11Earthquake Waves • Both transverse and longitudinal waves are produced when an earthquake occurs– S (shear) waves: Transverse waves that travel through the body of the Earth– P (pressure) waves: Longitudinal waves• Using the fact that only longitudinal waves goes through the core of the Earth, we can conclude that the core of the Earth is liquid– While in solid the atoms can vibrate in any direction, they can only vibrate along the longitudinal direction in liquid due to lack of restoring force in transverse direction.• Surface waves: Waves that travel through the boundary of two materials (Water wave is an example)Î This inflicts most damage.Monday, May 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon Yu12The Richter Earthquake Scale• The magnitude of an earthquake is a measure of the amount of energy released based on the amplitude of seismic waves. • The Richter scale is logarithmic, that is an increase of 1 magnitude unit represents a factor of ten times in amplitude. However, in terms of energy release, a magnitude 6 earthquake is about 31 times greater than a magnitude 5.– M=1 to 3: Recorded on local seismographs, but generally not felt – M=3 to 4: Often felt, no damage – M=5: Felt widely, slight damage near epicenter – M=6: Damage to poorly constructed buildings and other structures within 10's km – M=7: "Major" earthquake, causes serious damage up to ~100 km (recentTaiwan, Turkey, Kobe, Japan, California and Chile earthquakes). – M=8: "Great" earthquake, great destruction, loss of life over several 100 km (1906 San Francisco, 1949 Queen Charlotte Islands) . – M=9: Rare great earthquake, major damage over a large region over 1000 km (Chile 1960, Alaska 1964, and west coast of British Columbia, Washington, Oregon, 1700).Monday, May 3, 2004 PHYS 1441-004, Spring 2004Dr. Jaehoon
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