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Waves

Waves. Transverse: The medium oscillates perpendicular to the direction the wave is moving. Water (more or less) The “Wave”. Longitudinal: The medium oscillates in the same direction as the wave is moving Sound. Types of Waves. 8.

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Waves

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  1. Waves

  2. Transverse: The medium oscillates perpendicular to the direction the wave is moving. • Water (more or less) • The “Wave” • Longitudinal: The medium oscillates in the same direction as the wave is moving • Sound Types of Waves 8

  3. Period: The time T for a point on the wave to undergo one complete oscillation. • Speed: The wave moves one wavelength  in one period T so its speed is v = / T. Period and Velocity 22

  4. 5m Slinky Question Suppose that a longitudinal wave moves along a Slinky at a speed of 5 m/s. Does one coil of the slinky move through a distance of five meters in one second? 1. Yes 2. No 12

  5. Wavelength  Amplitude A A Harmonic Waves Wavelength: The distance  between identical points on the wave. Amplitude: The maximum displacement A of a point on the wave. Angular Frequency w:w = 2 p f Wave Number k: k = 2 p / l Recall: f = v / l y x 20

  6. Example: microwave • The wavelength of microwaves generated by a microwave oven is about 3 cm. At what frequency do these waves cause the water molecules in your burrito to vibrate ? The speed of light is c = 3x108 m/s 29

  7. Interference and Superposition • When too waves overlap, the amplitudes add. • Constructive: increases amplitude l2-l1 = m λ • Destructive: decreases amplitude l2-l1 = (m+1/2) λ 34

  8. Example: two speakers • Two speakers are separated by a distance of 5m and are producing a monotone sound with a wavelength of 3m. Other than in the middle, where can you stand between the speakers and hear constructive interference?

  9. Example: two speakers • Two speakers are separated by a distance of 5m and are producing a monotone sound with a wavelength of 3m. Where can you stand between the speakers and hear destructive interference?

  10. Reflection Act • A slinky is connected to a wall at one end. A pulse travels to the right, hits the wall and is reflected back to the left. The reflected wave is A) Inverted B) Upright • Fixed boundary reflected wave inverted • Free boundary reflected wave upright 37

  11. Standing Waves Fixed Endpoints • Fundamental n=1 • ln = 2L/n • fn = n v / (2L) 44

  12. Velocity of Waves on a string µ = mass per unit length of string As µ increases, v decreases, f decreases (λ fixed) 17

  13. Example: guitar A guitar’s E-string has a length of 65 cm and is stretched to a tension of 82N. If it vibrates with a fundamental frequency of 329.63 Hz, what is the mass of the string? 48

  14. Summary • Wave Types • Transverse (eg pulse on string, water) • Longitudinal (sound, slinky) • Harmonic • y(x,t) = A cos(wt –kx) or A sin(wt – kx) • Superposition • Just add amplitudes • Reflection (fixed point inverts wave) • Standing Waves (fixed ends) • ln = 2L/n • fn = n v / 2L 50

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