Goal: to understand waves

1. Goal: to understand waves Objectives: To learn about Oscillations and vibrations To understand the properties of Waves To learn about Transverse waves To understand Interference To learn about how to use waves scientifically

2. Pendulum • One form of oscillation is a pendulum. • You tie a mass to the end of a string. • You pull that object up so that it has some potential energy. • You let it go. • What happens? • Will the motion depend on the mass of the object on the string (assuming we can ignore the mass of the string)?

3. Period • The time it takes the pendulum to do a full move back and forth is called the oscillation period. • The period does NOT depend on mass! • The period only depends on the length of the pendulum (assuming a small movement back and forth).

4. Springs • Since you will look at these in lab I will cover this briefly (not in book though). • Springs pull or push things to some equilibrium point (see drawings on board). • If you compress the spring past this, it will push you back. • If you pull it past this it will push you in.

5. Frictionless spring • Lets imagine a horizontal spring with a weight attached to it which is pulled out past the equilibrium point. • What direction is the force (no we will not cover the amount of force even though that is a somewhat straightforward equation)? • What direction will the mass be moved?

6. A bit later • The force the spring applies depends on the distance from the equilibrium point. • The further away from that point the bigger the force. • How will the magnitude of the force change with time? What about the direction?

7. At equilibrium point • What will the force be? • What will the acceleration be? • What is the direction (if any) of motion?

8. Past equilibrium point • Lets say you started 0.2 m from the equilibrium point. How far to the other side of the equilibrium point do you think you will get?

9. Wave properties • (draw wave on board) • Waves have: • Period – how long it takes to complete wave • Frequency – how many waves you get every second (units are 1/seconds, or Hertz) • Period = 1 / Frequency • Wavelength – distance from crest to crest or trough to trough • Amplitude – height of the wave • Velocity – how fast the wave moves

10. Transverse waves • Transverse waves are waves that propagate in a direction ahead, but the wave is caused by a motion perpendicular (aka side to side). • An example is a string moved back and forth.

11. Standing Waves • Not in the book, but lets take a look. • Standing waves are waves that have “nodes” that stay in place. • Nodes are points that don’t move. • For this to happen, how much my wavelength compare to the length of my spring/string?

12. Wave speed • The velocity that waves move is called wave speed. • Wave speed = wavelength * frequency

13. Longitudinal (compression) waves • These are waves that compress the local region. • Examples of this are sound waves and Spiral Arms in Astronomy.

14. Interference • If you toss two rocks at each other, they collide. • If two waves cross each other, they pass through, by they do interfere at that point. • The two waves add.

15. Constructive interference • If the waves are positive at the same time and negative at the same time they will make a bigger wave. • This is called constructive interference. • Can you think of a use for this? • When would this be a bad thing?

16. Destructive interference • If the waves are opposite to each other then when you add them you get a smaller wave, or sometimes no wave at all. • This is called destructive interference. • When would this be a good thing? • When is this a bad thing?

17. During the 10 min break • So far we have examined waves emitted by a stationary source. • What happens if the source moves?

18. Scientific Use 1: Doppler Shift • When a source of waves moves you have what is called a Doppler shift. • Think to when you are creating a wave. • The front part of the wave will move away from you at some constant wave speed. • However, the position of the end of the wave depends on where you are when you FINISH the wave. • So, if you move forward, the wave will be shortened. • If you move backwards the wave will be lengthened. • The amount of the change of the wave will just depend on how far you move in the time that it takes to make the wave.

19. Doppler equation • So, the equation is: Actual wavelength = Stationary wavelength * ( 1 – velocity / wave speed) • And if the source is moving towards you (positive velocity) then the wavelength is “blue-shifted” because the wavelength shrinks. • If it moves away (negative velocity) then the wavelength is “red-shifted” because the wavelength increases.

20. Train/Indy Car • Imagine a train or an Indy car moving towards you. • While it moves towards you any noise it makes is “blue-shifted” – which means it goes to higher frequency (shorter wavelength means higher frequency). • Once it passes you it is moving away from you, so the noise is then “red-shifted” – which means it goes to lower frequency.

21. Uses for Doppler Effect • Brainstorm some uses for the Doppler Effect with your neighbors. • No, the answers are not on the next slide so that you can look them up and not think about them…

22. Shock Waves • One side effect of the Doppler effect is Shock Waves. • Imagine that you are moving FASTER than the wave speed. • When you finish the wave, you will be AHEAD of the start of the wave! • In this case the waves are focused behind you at a single point (instead of spread out continuously). • This creates a shock wave.

23. In: • In water this creates a “bow shock”. This is a triangular shock wave that you commonly see around boats. • In air this creates a “sonic boom” as all the sound comes at you at once instead of over time. • For light: no mass can travel at light speed, let alone travel faster, so there is no “light boom” – thankfully. If there was, it would probably involve time itself.

24. Scientific Use 2 - seismology • Earthquakes are waves that pass through the earth. • A fault acts like my hand moving the spring back and forth. • Earthquakes actually cause not 1 but 2 waves. • The P wave are compression waves and can move anywhere. • S waves go side to side (they do the shaking) and can only move through solids.

25. What can we learn from earthquakes? • A lot actually. • The first thing is that we look at the P and S waves go through the center of the earth. • From this we can tell that there is a liquid portion of our core (as the S waves don’t go through that). • Also, different materials, and different densities/phases have different wave speeds. • So, if we measure how long it takes the P waves to go in different directions through the core then we can tell what the core is made of, and what its temperature and densities are.

26. Also • We can use smaller man made “quakes” on the surface of the earth to find materials such as oil.

27. Conclusion • We have learned a lot about waves. • We have learned the properties of waves. • We have seen 2 ways of creating waves (transverse and compression). • We have found ways to use these waves to arrive at scientific discoveries.