Chapter 11: Waves

*Chapter 11: Waves

*Intro to Waves

*Wave vs particle*Mechancal vs non-mechancal*Longitudinal vs Transverse*Spreading of waves

* I. Nature of a WaveA. Definition of wave

*A disturbance which travels through a medium from one point in space to the others.*A medium is the matter through which a wave travels*E.g. pond- water; sound- air; earthquake- Earth

*Mechanical waves- require a medium*Electromagnetic waves- do not require a medium; instead

these waves consist of changing electric and magnetic fields*E.g. light and radiowaves

*Properties of Waves

*Energy is transferred from one place to another in a wave motion. * WAVES TRANSFER ENERGY!

*Motion of the medium (particles of the medium) is usually periodically vibratory.

*Only the shape or form of wave travels, not the medium.*Energy may spread out as waves travel (drop pebble, circles get larger as they spread outwards)

*VibrationsVibrational Motion*Vibration: in a general sense, anything that switches back and forth, to and fro, side to side, in and out, off and on, loud and soft, or up and down is vibrating. A vibration is a wiggle in time.*Wave: a wiggle in both space and time is a wave. A wave extends from one place to another.*Vibrations and waves: the source of all waves is something that is vibrating. Waves are propagations of vibrations throughout space. *Harmonic motion occurs when a vibration repeats and is converted (no energy input is needed to continue the motion)

*Harmonic Motion

• A wave is an oscillation that travels.

• A ball floating on water can oscillate up and down in harmonic motion.

• The surface of the water oscillates in response and the oscillation spreads outward from where it started.

* B. Properties of Periodic Motion • Cycle: A cycle is a unit of motion that repeats.

* B. Categories of Waves

Waves are classified into different types according to their natures :

T ra ns ve rs e w a ve s L o ng itu d ina l w a ve s

Mechanical w aves

T ra ns ve rs e w a ve s

Elec tromagnetic w aves

WA V E S

* 1. Classification based on direction of vibration

• According to the direction of vibration, waves are classified into : (a) Transverse wave; ( doing ‘the wave’, string on a door knob)

(b) Longitudinal waves (sound waves, sslinky- stretch and move directly toward the end)

ONLINE DEMO: http://www.acoustics.salford.ac.uk/schools/teacher/lesson1/lesson1interactive.html

*a. Transverse Waves*The waveform appears in the shape of sine curve.*A wave in which the motions of the matter particles are

perpendicular to the direction of propagation of the wave itself.

Water waves, pulse in a stretched string,transverse wave demonstrator.

Examples

* b. Longitudinal Waves

*A wave in which the motions of the matter particles are in the same direction as the wave propagation.

ExamplesSound, or a spring oscillating up and down

* 2. Based on medium a. Mechanical Waves

*A material medium is necessary for the transmission for mechanical waves. Mechanical waves cannot travel through vacuum.*Due to forces on particles in the “medium” that are next to each other, the

disturbance is transmitted from one layer to the next through the medium.

*b. Non Mechanical Waves (Electromagnetic Waves)*Material medium is not essential for propagation. e/m waves travel through vacuum.*Disturbance of electric and magnetic fields travelling through space.*All electromagnetic waves are transverse waves.

X-rays, radio waves, micro-waves,etc. examples

*A. Anatomy of a Wave

*Amplitude *Wavelength ()*Frequency (f)*Period (T)*Wave velocity (v)

A wave is usually described by the following terms :

Each term will be explained….

*The amplitude is the maximum displacement of the medium from its equilibrium position. The amplitude of a wave refers to the distance from the equilibrium point (or ½ the distance from highest to lowest point of vibration)*The wavelength () is the minimum distance between two points

which are in phase.*The frequency (ƒ) is the number of complete oscillations made in one

second. The frequency of a wave refers to how many “waves” pass by a point in a given amount of time (usually a second) Unit : Hz *The period (T) The period of a wave is the time for a to make one

complete cycle. Period, being a time, is measured in units of time such as seconds, hours, days or years. It is the time taken for one complete oscillation. It is related to frequency by T = 1/ƒ Unit : s

*Graphing harmonic motion- using paper and string

*When oscillations are small, the motion is called simple harmonic motion (shm) and can be described by a simple sine curve.*See animation

*Transverse Paper Activity

* Use construction paper- string -glue* create a transverse wave * Label parts*Crest‘- highest part off rest of transverse wave* Trough-lowest part off rest of transverse wave* Amplitude-maximum displacement off rest*Wavelength-distance between two points –crest to crest* Frequency- to how many “waves” pass by a point in a

given amount of time (usually a second)the entire sheet is one second

* Period-time for a wave to make one complete cycle.

*Longitudinal wave

*Longitudinal paper activity

* Flip side of transverse wave model* create a longitudinal wave – draw slinky-like model* Label parts* Compression-Crest- particles – highest density* Rarefaction -Trough-particles stretched* Amplitude-maximum displacement off rest-compression to rest* Wavelength-distance between two points –compression to

compression* Frequency- to how many “waves” pass by a point in a given

amount of time (usually a second)the entire sheet is one second

* Period-time for a wave to make one complete cycle.

E. The Wave EquationThe wave velocity is the displacement traveled by the wave in one second ……....

The wave velocity (v) is related to frequency and wavelength by --

v = ƒThe Wave Equation

Using the Wave EquationExample :A travelling wave of wavelength 0.6m moves at a speed of 3.0 m/s. What is the period of this wave ?

Then the period of this wave is ???Period T = 1/ƒ T = 1/5.0 or 0.2 s

= 0.6 m, v = 3.0 m/sf = ?

By using the wave equation, v = ƒ ƒ = v/ f = (3.0 m/s)/(0.6 m) ƒ = 5.0 Hz

The unit of ‘m’ cancel out—

and you are left with 5.0/s

which is 5.0 Hz

*Relationship between speed, frequency, and

wavelength*The speed of a wave equals the frequency times the wavelength.

v = f Frequency (cycles/sec)

Wavelength (m)

Speed (m/sec)

*A student does an experiment with waves in water. *The student measures the wavelength of a wave to be 5 centimeters. *By using a stopwatch and observing the oscillations of a floating ball, the student measures a frequency of 4 Hz. *If the student starts a wave in one part of a tank of water, how long will it take the wave to reach the opposite side of the tank 2 meters away?

*WAVE EQUATION ACTIVITY

*Calculate the wave equation using graph paper model activity

*Sine curve- draw 1,2,4,5,10, 20 waves – each wave has an amplitude of 2 blocks to crest and 2 blocks to trough.

CALCULATE:*Frequency-period*wavelength *Wave speed

*SLINKY LAB