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Waves: Transverse and Longitudinal in Physics 101

This lecture discusses the concepts of transverse and longitudinal waves, including their properties such as wavelength, amplitude, and frequency. It also covers topics like interference, reflection, and standing waves. Examples and calculations are provided to enhance understanding.

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Waves: Transverse and Longitudinal in Physics 101

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  1. Final Physics 101: Lecture 20 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 increases, 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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