Harmonic Motion & Waves
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1 Harmonic Motion & Chapter 25 Harmonic Motion What is it and why is it important? Harmonic Motion Any motion that is cyclical; that repeats itself. Pendulum or swing Wheel Frequency (f) The number of vibrations that occur per second f = vibrations/second or cycles/second unit: Hertz (Hz) ( 1/sec or sec 1 ) Harmonic Motion Period (T) How long it takes to make one complete vibration or cycle. unit: Seconds T = 1 / f or A Pendulum has a frequency of 60 Hz. How many vibrations does it make in one second? How long does it take to make one vibration? (T) 1
2 Graphs of Harmonic Motion Most harmonic motion is represented by a wave. The closer the waves crest, the shorter the period and the higher the frequency. Wave Characteristics Amplitude (A) The larger the waves the greater the Amplitude Zero A speaker moves in and out. The louder it gets the greater the distance between the in and out positions. Maximum Minimum Larger Amplitude Smaller Amplitude Amplitude is the height from the mid-point line to the top or bottom of the wave. Wavelength ( ) Distance between identical points. Just like period measured from the same points on the wave Crest to crest Trough to trough Zero to zero 2
3 Wave Speed All waves of the same type travel at the same speed in a given medium; sound waves travel at the same speed in air light waves travel at the same speed in water. v = f Velocity equals wavelength * frequency What is the speed of a sound wave that has a wavelength of 0.68 m and a frequency of 500 Hz? 0.68m/cycle * 500 cycle/sec = 340 m/sec For any given medium, if Frequency increases, Wavelength decreases and if Frequency decreases, Wavelength increases BUT the speed remains the same Types Transverse Wave The vibrational motion of the wave is perpendicular to the wave s direction. Longitudinal Wave The vibrational motion of the wave is in the same direction as the wave s direction. Interference When two waves meet they combine, and we say they interfere. Constructive Interference When both waves add to each other Destructive Interference When both waves subtract from each other
4 Acoustics and Vibration Animations - Dan Russell, Kettering University Beats Constructive and destructive interference. In Phase Constructive (amplitude increases) Out of Phase Destructive (amplitude decreases) What about a combination of in phase and out of phase? Paul Hewitt BEATS A combination of constructive and destructive interference results in a pulsation in the amplitude. interference applet Beats applet Standing If a series of waves are generated and reflect off a hard surface, the reflected wave and the original wave will combine. Node A point where the two waves cancel one another (trough meets crest.) Antinode A point where the two waves reinforce one another (trough meets trough, or crest meets crest.) Wave 1 is only ½ a wavelength. Wave 2 is a full 1 meter wavelength. 1 meter Wave 3 is 1 ½ wavelength Wave 4 is 2 wavelengths Frequency of beat is frequency (264 hz-260 hz = 4 beats/second) What is the wavelength of waves 1,3,5? 4
5 Acoustics and Vibration Animations - Dan Russell, Kettering University Interactions Reflection When a wave bounces off surface. Diffraction The bending of a wave as it goes through a small opening or around a corner. Reflection and Refraction Refraction The bending of a wave as it passes from one medium to another due to a change in the speed of the wave as it goes into the new medium. Light is the best example, it bends as it goes from air into water or water into air. It slows down in the water, and speeds up in the air. Sound also undergoes refraction Resonance Resonance The frequency at which the amplitude of a system increases. If the applied force has the right frequency, it will cause the system to vibrate
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