Goal: to understand waves Objectives: 1)To learn about Oscillations and vibrations 2)To understand the properties of Waves 3)To learn about Transverse waves 4)To understand Interference 5)To learn about how to use waves scientifically

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)?

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).

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.

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?

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?

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

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?

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

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.

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?

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

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

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.

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?

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?

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

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.

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.

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.

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…

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.

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.

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.

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.

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

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.