Determining Wave Speed

1. Determining Wave Speed • Universal Wave Equation

2. Example – calculate wave speed A harp string supports a wave with a wavelength of 2.3m and a frequency of 220.0 Hz. Calculate its wave speed

3. Example – calculate wavelength • A trumpet produces a sound wave that is observed travelling at 350 m/s with a frequency of 1046.50 Hz. Calculate the wavelength of the sound wave.

4. Factors that affect wave speed • Temperature • Linear Density

5. Reflection • What will happen to the wave pulses shown below? • Link to video (blip.tv) A: Wave pulse heading towards a wall. B: Wave pulse heading towards a “free end”.

6. Reflection & Transmission • When a wave moves from one medium to another, its speed changes but its frequency remains the same. • What else happens when waves move from one medium to another? What will happen to the pulses shown below? B: Wave pulse travelling from a thicker rope into a thinner rope.(More Dense  Less Dense, Slower  Faster) A: Wave pulse travelling from a thinner rope into a thicker rope.(Less Dense  More Medium, Faster  Slower)

7. Interference of Waves • Principle of Superposition:The resultant displacement is the sum of the displacements of each component wave.

8. Interference of Waves • What happens after the waves interfere with each other?

9. Interference of Waves • What happens when the wave pulses shown below meet? • Principle of Superposition:The resultant displacement is the sum of the displacements of each component wave.

10. Interference of Waves

11. Interference of Waves • Constructive interference:Resultant displacement is greater than individual pulses. • Destructive interference:Resultant displacement is smaller than individual pulses.

12. Interference of Waves

13. Standing Waves • When identical periodic waves travel in opposite directions, they produce a pattern that appears to be standing still. Such waves are known as standing waves. • Parts of a standing wave • Nodes • Points on wave that never move • Located half wavelength apart • Antinodes • Points that vibrate maximally

14. Standing Waves • The standing waves can be produced using one source:a 2nd identical wave is produced by reflection. • For every medium of fixed length, there are many natural frequencies that produce resonance:

15. Standing Waves • Fundamental frequency • Lowest natural frequency, longest wavelength • Also called fundamental mode • Overtones • Refer to all natural frequencies higher than the fundamental • 1st overtone = 1 node, etc. • Harmonics • Refer to fundamental & any overtone • Fundamental = 1st harmonic,1st overtone = 2nd harmonic, etc.

16. Harmonics

17. Practice • P. 391 # 1-6

18. Recap: Properties of Waves • Reflection • Transmission • Require a medium in which to travel • Interference (Principle of Superposition) • Exhibit constructive & destructive interference What are some other properties of waves?

19. Law of Reflection • The angle of incidence is equal to the angle of reflection: A water wave incident on a barrier. The dotted line is called the “normal”. The normal line by definition is perpendicular to the barrier. All angles are measured from the normal.

20. Refraction • When waves travel from one medium into another, their speed changes. • This causes the wave to bend: When water waves travel from deep to shallow water, the speed of the wave decreases. Since the frequency of waves is constant, because the wave’s speed decreases, its wavelength decreases. (Why?) Waves travelling from a faster to a slower medium always bend towards the normal.

21. Diffraction • When waves travel past the edges of a barrier or through a small opening, waves bend & spread: • The amount of diffraction is greatest when the size of the opening is the approx. equal to the wavelength.

22. 2D Interference

23. 2D Interference