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# Vibrations and Waves

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1. Vibrations and Waves Vibration: a repeating back-and-forth motion A vibration cannot exist in an instant Wave: a disturbance that repeats regularly in space and time A wave is a vibration in space and time Waves move energy from one position to another, not matter. Ex: Light and sound

2. Partsof a Sine Wave Sine wave: a pictorial representation of a wave. Crest: the highest part of a sine wave Trough: the lowest part of a sine wave Amplitude: The distance from the midpoint to the crest or from the midpoint to the trough. • The greatest vertical movement of the wave • SI unit: meters (m)

3. Sine Wave

4. Wavelength: the distance between successive identical parts of a sine wave. • How far until a wave repeats itself • Ex: crest to crest, trough to trough • SI unit: meters (m)

5. Energy of a Wave • The energy transferred from a vibrating source is carried by a disturbance in the medium, not by matter moving from one place to another. • Waves moveENERGY, not matter • Energy carried by a wave consist of KE and PE

6. In a pendulum, the greatest KE is at the bottom of the swing • This would be the middle (equilibrium line) of a sine wave • The greatest PE is at the tallest points of the swing • This would be the crest and trough of a sine wave • The total energy of wave remains the same • At the crests and troughs, there is the most PE and the least KE • At the middle, there is the most KE and the least PE

7. Period and Frequency Period: the time required to complete one cycle. • The time for a wave to repeat itself • SI Unit: seconds (s)…same as for time • Period of a pendulum: • The time of a back and forth swing • The period depends ONLY on: • the length of the pendulum • A long pendulum has a longer period than a shorter pendulum. • the acceleration due to gravity.

8. Check Your Understanding Which will have a greater period, a pendulum with a 5 kg mass on 1 m of string or a pendulum with a 10 kg mass on 1 m of string? • Neither! They both have the same period because they both have the same length. Mass has NO affect on the period of a pendulum.

9. Frequency: How frequently a vibration occurs. • # waves per second • Unit: Hertz (Hz) which means per second (1/s). • If the frequency of a vibrating object is known, its period can be calculated and vice-versa. • The frequency and period are inverses of each other. f = 1/T T = 1/f • f = frequency • Measured in Hertz (Hz) • T = period • Measured in seconds (s)

10. Check Your Understanding What is the frequency in vibrations per second of a 100 Hz wave? • 100 Hz vibrates 100 times per second The Sears Building in Chicago sways back and forth at a frequency of about 0.1 Hz. What is the period of vibration? • T=? f = 0.1 Hz T = 1/f T = 1/0.1 = 10 seconds

11. Transverse Waves Transverse wave: a wave with a vibration at right angles to the direction the wave is traveling. • The energy moves through the medium left to right, but the motion of the wave is up and down • Makes an “S” shape wave • Ex: light waves, string instrument

12. Longitudinal Waves Longitudinal wave: a wave in which the vibration is in the same direction as that which the wave is traveling. • Both the energy motion and the movement of the wave are left to right • Makes a pulse through the wave • Ex: sound waves, earthquake waves

13. Interference • An interference pattern is formed by the overlapping of two or more waves that arrive in a region at the same time. • There are 2 types of interference • Constructive interference • Destructive interference

14. Constructive Interference Constructive interference: addition of two or more waves when wave crests overlap to produce a resulting wave of increased amplitude • The amplitude of the two original crests are combined to add to the new amplitude • Ex: A noisy room (several sound waves adding at the same time)

15. Destructive Interference Destructive interference: combination of waves where the crests of one wave overlap troughs of another, resulting in a wave of decreased amplitude. • The amplitude of the original waves are subtracted because they are in opposite directions • Ex: anti-noise technology cancels out sound

16. Principle of Superposition Principle of Superposition: the displacement of a medium caused by two or more waves is the algebraic sum of the displacements caused by the individual waves • When two waves interfere with each other, the combined amplitude depends on the direction and height of the amplitude of the original wave. • Ex: subtracting amplitudes with destructive interference, adding amplitudes with constructive interference

17. Check Your Understanding Two waves reach the same place at the same time. One has an amplitude of 2 m up and the other has an amplitude of 3 m up. What type of interference is this? • Constructive interference b/c both amplitudes are in the same direction. What is the new amplitude? • Because they are up going up, you add the amplitudes. 2 + 3 = 5 m

18. Check Your Understanding Two waves reach the same place at the same time. One has an amplitude of 4 m up and the other has an amplitude of 4 m down. What type of interference is this? • Destructive interference b/c the amplitudes are in opposite directions. What is the new amplitude? • 4 – 4 = 0 m. There is no amplitude!

19. The Doppler Effect Doppler effect: the change in frequency due to the motion of the source or the receiver. • The greater the speed of the source, the greater the Doppler effect will be. • Ex: the shift in pitch of a siren as it drives past you

20. The Doppler Effect for Sound • The pitch of sound is higher when the source moves toward you, and lower when the source moves away from you. • Pitch is the same as frequency • As a source (like a siren) and a receiver (like you) move closer together, the pitch increases b/c the frequency increases • As a source (like a siren) and a receiver (like you) move away from each other, the pitch decreases b/c the frequency decreases