1. Topic 4 Waves

2. What is a wave?

3. Waves Waves transfer energy without a net motion of the medium through which they travel. They involve vibrations (oscillations) of some sort.

4. Wave fronts Wave fronts highlight the part of a wave that is moving together (in phase). = wavefront Ripples formed by a stone falling in water

5. Rays Rays highlight the direction of energy transfer.

6. Transverse waves The oscillations are perpendicular to the direction of energy transfer. Direction of energy transfer oscillation

7. Transverse waves crest trough

8. Transverse waves Water ripples Light On a rope/slinky Earthquake

9. Water Waves

10. Longitudinal waves The oscillations are parallel to the direction of energy transfer. Direction of energy transfer oscillation

11. Longitudinal waves compression rarefaction

12. Longitudinal waves Sound Slinky Earthquake

13. Displacement - x This measures the change that has taken place as a result of a wave passing a particular point. Zero displacement refers to the equilibrium (average) position. = displacement

14. Amplitude - A The maximum displacement from the mean position. amplitude

15. Period - T The time taken (in seconds) for one complete oscillation. It is also the time taken for a complete wave to pass a given point. One complete wave

16. Frequency - f The number of oscillations in one second. Measured in Hertz. 50 Hz = 50 vibrations/waves/oscillations in one second.

17. Wavelength - λ The shortest distance between points that are in phase (points moving together or “in step”). wavelength

18. Wave speed - v The speed at which the wave fronts pass a stationary observer. 3 x 10 8 m.s -1

19. Period and frequency Period and frequency are reciprocals of each other f = 1/TT = 1/f

20. The Wave Equation The time taken for one complete oscillation is the period T. In this time, the wave will have moved one wavelength λ. The speed of the wave therefore is distance/time v = d = λ = fλ t T

21. Example The ocean wave below completes one full oscillation in 2 seconds. a. What is the amplitude? b. What is the wavelength? c. What is the period? d. What is the frequency? e. What is the wave speed? Displacement m 1 2 1.41.51.61.7 -2

22. Example The ocean wave below completes one full oscillation in 2 seconds. a. What is the amplitude? 2 m Displacement m 1 2 1.41.51.61.7 -2

23. Example The ocean wave below completes one full oscillation in 2 seconds. a. What is the amplitude? 2 m b. What is the wavelength? 0.3 m Displacement m 1 2 1.41.51.61.7 -2

24. Example The ocean wave below completes one full oscillation in 2 seconds. a. What is the amplitude? 2 m b. What is the wavelength? 0.3 m c. What is the period? 2 s Displacement m 1 2 1.41.51.61.7 -2

25. Example The ocean wave below completes one full oscillation in 2 seconds. a. What is the amplitude? 2 m b. What is the wavelength? 0.3 m c. What is the period? 2 s d. What is the frequency? f = 1/T = 1/2 = 0.5 Hz Displacement m 1 2 1.41.51.61.7 -2

26. Example The ocean wave below completes one full oscillation in 5 seconds. a. What is the amplitude? 2 m b. What is the wavelength? 0.3 m c. What is the period? 5 s d. What is the frequency? f = 1/T = 1/5 = 0.2 Hz e. What is the wave speed? v = fλ = (0.5)(0.3) = 0.15 ms -1 Displacement m 1 2 1.41.51.61.7 -2

27. 1)A water wave has a frequency of 2Hz and a wavelength of 0.3m. How fast is it moving? 2)A water wave travels through a pond with a speed of 1m/s and a frequency of 5Hz. What is the wavelength of the waves? 3)The speed of sound is 330m/s (in air). When Dave hears this sound his ear vibrates 660 times a second. What was the wavelength of the sound? 4)Purple light has a wavelength of around 6x10 -7 m and a frequency of 5x10 14 Hz. What is the speed of purple light? Some example wave equation questions 0.2m 0.5m 0.6m/s 3x10 8 m/s /s v = fλ = 2Hz ∙ 0.3m = λ = v/f = 1m/s / 5Hz = λ = v/f = 330m/s / 660Hz = v = fλ = 5x10 14 Hz ∙ 6x10 -7 m