1. 1 Honors Physics 1 Lecture 21 - F2013 Waves –Terms –Travelling waves –Waves on a string

2. 2 Waves Overview A wave is a disturbance that moves through a medium. –manifestations –common language of waves »amplitude, period, frequency, wavelength, speed –special case: waves on a string »speed, energy transmission, interference, standing waves and resonance –sound waves »mechanism, speed, intensity, beats

3. 3 Mechanical waves e.g. - water, sound, seismic, string, drumhead transmitting effect: forces between atoms and molecules moves through: matter Electromagnetic waves e.g. – radio; microwave; infrared,visible and ultraviolet light; x-rays; gamma rays moves through: vacuum Matter waves All the stuff around you - observable on very short length scales and for very light particles moves through: vacuum

4. 4 Classifications of waves Transverse wave – the local displacement or field amplitude is perpendicular to the direction of energy flow –examples: string, drumhead, water surface

5. 5 Classifications Longitudinal waves – the local displacement or field amplitude is parallel to the direction of energy flow –examples: sound, Slinky™, seismic p-wave

6. 6 Terms: Periodic Waves amplitude period - T time If you’re sitting at one point* and watch the waves go by… f=1/T *e.g.- on the dock of the bay

7. 7 Terms: Periodic Waves amplitude wavelength - distance Freeze the waves in time and look at the shape…

8. 8 Harmonic waves A math fact: Any finite function can be represented as the sum of sine and cosine functions. So all we need to really understand is sine, or harmonic waves

9. 9 Harmonic travelling waves represents a wave of amplitude y max travelling in the + x direction.

10. 10 A travelling sine wave A point with a specific phase moves to the right at speed v. phase

11. 11 iClicker Check 21.1 Write the phase in terms of (x-vt) to get the speed.

12. 12 iClicker Check 21.2 The term that multiplies x is inversely proportional to wavelength.

13. 13 iClicker Check 21.3 The term that multiplies t is proportional to frequency.

14. 14 Phase and Phase Difference The argument of the sine fn: is called the phase of the wave. When we talk about phase difference , we are talking about how the argument differs for different times or places in the wave. For two times (at the same point): For two points (at the same time):

15. 15 Phase and phase difference

16. 16 Comparing two waves at different times t=0 A point of constant phase moves distance vt in time t. The phase at a point in space changes by:

17. 17 iClicker Check 21.4 Can you uniquely determine the velocity of a wave from snapshots of amplitude vs position at two different times? a)Yes b)No Because the wave repeats, the change in position can be altered by an integer times the wavelength and you won’t know the difference.

18. 18 Wave on a string 1

19. 19 String wave derivation

20. 20 Waves on a string 2

21. 21 In-class exercise

22. 22 Waves on a string 3

23. 23 iClicker question 21.4 When the tension in a string is increased, the wave speed A)Remains the same. B)Increases C)Decreases

24. 24 iClicker question 21.5 When the amplitude of motion of a wave on a string is increased (keeping tension, mass per length, amplitude the same), the wave speed A)Remains the same. B)Increases C)Decreases

25. 25 iClicker question 21.6 When the amplitude of motion of a wave on a string is increased (keeping tension, mass per length, amplitude the same), the transverse speed A)Remains the same. B)Increases C)Decreases