Goal to understand waves Objectives 1 To learn

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

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

Linear frequency vs angular frequency • Linear frequency (f) is how often an object does a full pulse per second (units Hertz) • Angular frequency (w) is how many radians the pulse cycles through each second (units rad/sec) • Yes, angular velocity and angular frequency are pretty much the same thing. • The conversion: w = 2π f

Quick sample • A wave has an angular frequency of 2. 4 rad/sec. • What is the linear frequency of the wave?

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 • 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 • On the shore of a lake 4 waves come by every 3 seconds. • The distance between the crests of the waves is 12 m. • A) What is the frequency of the waves? • B) What is the wave speed of the waves?

Another way to find speed • On a string: • V = (FL/m)1/2 • L is the length of string, m is the mass of the string, and F is the tension in the string • m/L = linear mass density = μ • So, another way to write the equation is: V = (F/ μ)1/2

Example from HW slightly redone • While using a land line telephone you flick the cord sideways. • The cord has a mass of 0. 1 kg and a length of 1. 2 meters. • If the wave takes 0. 2 sec to get to the end of the cord find: • A) the velocity of the wave (we have a distance and a time…) • B) The Tension of the phone cord

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

Equation for a wave • • • Y = A sin(kx + wt) A is the max amplitude X is the position W is the angular frequency of the wave k is the wave number of the wave (kx + wt) is the phase of the wave • The wavelength is set by kx = 2π • So, wavelength = 2π/k

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?

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.

If time • • • A string has a weight attached to the end of it of unknown mass. The string is vibrated at an angular frequency of 2 rad/sec. The wave number (k) = 0. 4 m-1 The string has a linear mass density of 0. 03 kg/m. There are 2. 5 waves on the string (drawn on the board). A) What is the wavelength of the waves? B*) What is the length of the string? C) What is the linear frequency of the waves? D*) What is the wavespeed of the waves? E*) If the tension is created by the weight at the end then what is the size of the unknown weight (this one is a bit tricky)? • * indicates similar to a homework question

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.