Chapter 19: Vibrations and Waves SIMPLE HARMONIC MOTION ic or Oscillatory motion is called SHM. Start off with the story of Galileo being in the church. PENDULUM Make the following points with a pendulum demo. 1. PERIOD time amount for one complete cycle or oscillation Other names are vibrations and to & fro 2. Make two pendulums of equal length but different in mass and ask the question: Does the period depend on the mass? Independence of Mass 3. Make two pendulums of unequal lengths with the same mass and ask the question: Does the period depend on the length? Dependence of Mass Summary: Longer length longer period Shorter length shorter period Conceptual example: our legs act like pendulums: Longer legs longer periods slower strides giraffes, ostriches shorter legs shorter periods faster strides dachshunds, mice mass-spring system 1. Equilibrium point spring force is balanced with weight 2. Crest and Trough mass is at the high and low points 3. Amplitude distance from equilibrium to maximum displacement 4. time distance from peak-to-peak or trough-to-trough, CHECK QUESTION Use a demo and ask which pendulum will have a longer period? (a) (b) vs. vs. Spring-harmonica system CHECK QUESTION What kind of motion do we have here? Simple harmonica motion FREQUENCY How often a vibration occurs is called the FREQUENCY. 1 Frequency = 19-1
Remarks: Frequency = 1 Use a pendulum to show 1 Hz, 2 Hz, and 3Hz frequency. Frequency = 1 vibration in 1 sec 1 vib/sec 1 Hertz = 1 Hz 10 vibration in 1 sec 10 vib/sec 10 Hertz = 10 Hz UNITS of frequency 1 vib/sec = 1 Hertz = 1 Hz 10 vib/sec = 10 Hertz = 10 Hz Higher frequency measurements are made in khz, MHz, GHz AM Radio khz FM Radio 88.9 FM = 88.9 MHz = 88,900,000 vib/sec (electrons are vibrating in the antenna) Telephones - GHz Tuning fork with water and strobe 1 CHECK QUESTION Electricity coming in from the outlet is coming at 60 Hz. What is the number of oscillations and what is the period of each oscillation? WAVES MOTION What is the cause of a wave? An oscillator! Use a spring-mass system to show a sine curve 1. Equilibrium point spring force is balanced with weight 2. Crest and Trough mass is at the high and low points 3. Amplitude distance from equilibrium to maximum displacement 4. Wavelength distance from peak-to-peak or trough-to-trough, 5. time distance from peak-to-peak or trough-to-trough, Examples: Ocean waves have wavelength in meters; Pond waves have wavelength in centimeters; Light waves have wavelength in nanometers WAVE MOTION 1. The Medium and Energy Transfer All Waves need a Medium in order to travel (sound waves require air whereas water waves require water). A medium is a system of coupled oscillators. Oscillators are stationary in space and oscillate with a particular period. A coupled oscillator is a series of stationary oscillators connected to each other. As one oscillator is disturbed, the connecting oscillator is also disturbed as well and is forced to oscillate the oscillators are said to be coupled. Picture wise, Single oscillator Coupled oscillators Web Coupled oscillators http://www.kettering.edu/~drussell/demos/coupled/coupled.html Wave Machine 19-2
A wave is a disturbance of energy in the medium that transfers its energy without the transfer of material (or medium). For example, in Chapters 7, one saw that PE and KE always required a movement of mass. This is not the case with waves. Energy can be transferred from a source to a receiver without the transfer of matter. Examples: wave machine rods are the medium and they do not move with the wave water waves the water oscillates about a local equilibrium point the wave at football games 2. Two types of waves Transverse waves the medium moves perpendicular to the wave motion Longitudinal waves the medium move parallel to the wave motion Web types of waves mention how the medium acts as coupled oscillators http://www.kettering.edu/~drussell/demos/waves/wavemotion.html wave machine and slinky 3. Wave Properties Since waves are coupled oscillators, they automatically have similar properties of a single oscillator, however, there will be additional ones. Oscillators have period and amplitude Waves have period and amplitude also, but new properties of wavelength and wave speed. When one speaks of waves it is more common to talk in terms of frequency not period. Frequency = f = how often a wave crest occurs Wavelength = λ = the space distance between repeated crests Wave speed = v = the speed at which a wave travels at. 4. Wave Speed and the Medium 19-3
Let s look at a wave pulse traveling down the wave machine. We will find that the speed of a periodic wave is related to the frequency and the wavelength of the waves. Remember that Speed = Distance time Analogy: Suppose that you are interested in measuring the speed of a train of freight cars rolling by you. To determine the speed of the train, one counts the number of cars passing by. Suppose that 3 cars past by in 3 second. The speed of the train is Distance 3 (length of a freight car) 3 10 m Speed = = = = 10m / s time total time 3 sec Another way to measures the speed is how fast a single car passes by. One then writes Distance (length of a single freight car) 10 m Speed = = = = 10m / s time time for one freight car to pass 1 sec In wave language, a single train a single wave = one wavelength time for a single car to pass period of a single wave Wavelength Wave Speed = = Wavelength Frequency Wave Speed = Wavelength Frequency v = λf For a fixed medium, the speed of the wave is always the same (constant and unchanging). Therefore, one finds the important relationship v = constant =λ f = λ f = λ f wave machine long waves low freq short waves high freq 5. Wave Interference INTERFERENCE When two waves overlap, wave patterns may increase, decrease, and even neutralize the effects. These effects are called INTERFERENCE. CONSTRUCTIVE DESTRUCTIVE 19-4
Note that when Constructive interference occurs the displacement of the waves is a maximum Destructive interference occurs there is no displacement of the waves The Principle of Superposition When two or more waves are present simultaneously at the same place, the resultant disturbance is the sum of the disturbances from the individual waves. Use a wave machine to create constructive and destructive interference patterns. When wave pulses are sent continuously, a special condition occurs called standing waves. The reason why they are called standing waves is because they appear to be standing still. Standing waves happen for both transverse and longitudinal waves. Again, constructive means maximum displacement, whereas destructive means no displacement. NODE destructive interference is occurring ANTINODE constructive is occurring Animation Standing waves on a string http://cnx.org/content/m12589/latest/transversenodes.swf Use the wave machine to produce standing waves 19-5
Let s identify some nodes and antinodes I now want to show you some examples of nodes and antinodes. 1. Standing waves using the wave driver 2. Standing waves on Chlandni plates Doppler Applet http://www.astro.ubc.ca/~scharein/a311/sim.html#doppler 19-6