An Introduction To The Behavior Of Waves

An introduction to the behavior of waves Advanced level Physics AS

Sanjitha N. Adikari

Principle of superposition 

Where two or more waves meet , the total displacement at any point is the vector sum of the displacement that each individual waves would cause at that point.

Resultant wave

Individual waves Sanjitha N. Adikari

Principle of superposition theorem Vector sum means Waves in turn depends upon the path different between the waves involved.

Sanjitha N. Adikari

Sanjitha N. Adikari

Classifying waves 

Progressive waves  The

position of its perks and troughs are moving.  These waves have a property to carry energy ( action at a distance) 



Eg: pebble thrown in to the water cause a water waves spared out over the surface of water container.

Stationary waves ( standing waves)  The

wave is not progressive. Its perks and troughs aren't moving.  These waves have a property to create oscillation. 

Eg: guitar string, understanding the behavior of electrons and sub atomic particles Sanjitha N. Adikari

Stationary waves Rubber cord

vibrator

1 Wight to make a tension on string



As the frequency of the cord is increased resonance (the tendency of a system to oscillate at maximum amplitude at certain frequencies) occurs. Sanjitha N. Adikari



Stationary waves in a pipe.

closed end pipe

Open end pipe Sanjitha N. Adikari

Reflection at the end of string 

Setting up waves on a rope Fixed end

Free end

As the pulse reaches the end of the string the string exerts a force on the support. the support exerts a force equal in size but opposite in direction on the string. • The phase change on reflection occurs where a “hard” reflection occurs. Fixed End) • No phase change on reflection occurs where a “hard” reflection occurs. Fixed End) Sanjitha N. Adikari

air

glass

glass

air

If a wave traveling form a less dense medium to a more dense medium there is a PHASE CHANGE OF 180o

If a wave traveling form a more dense medium to a less dense medium there is a NO PHASE CHANGE.

D1

D2

D2

D2>D1 Sanjitha N. Adikari

D1

Reflection at a Point where the Wave Velocity Changes v2 > v1

Transmitted wave, no phase change. Reflected wave, phase change.

v2< v1 Transmitted wave, no phase change. Reflected wave, no phase change.

Sanjitha N. Adikari

Harmonics 

There are several frequencies with which the snaky can be vibrated to produce the patterns. Each frequency is associated with a different standing wave pattern. These frequencies and their associated wave patterns are referred to as harmonics.

Sanjitha N. Adikari



First Harmonic (Fundamental Frequency of Resonance)

All points oscillate in phase but with different amplitudes of oscillation. Consider the string to be disturbed at A (the centre). Waves travel towards B (and C) and are reflected with a 180° phase change. If the "effective distance" travelled by the waves is l, then resonance occurs. This means that, for the first resonance, the distance A B A (or A C A) must be equal to l/2.



second Harmonic (Frequency of Resonance) Sanjitha N. Adikari

Organ

Sanjitha N. Adikari



Nodes -The crests and troughs of a standing wave do not travel, or propagate, down the string. Instead, a standing wave has certain points, called nodes, that remain fixed at the equilibrium position.



Antinodes These are points where the original wave undergoes complete destructive interference with its reflection. In between the nodes, the points that oscillate with the greatest amplitude—where the interference is completely constructive—are called antinodes.

Antinodes

Nodes

Sanjitha N. Adikari

Finding the frequencies of the harmonics 

To find the frequencies of the harmonics for a stretched string. We can use the fact that the speed at which a transverse wave is propagated along a string. 

V = T/µ  µ -Mass per unit length  T- tension

Sanjitha N. Adikari



We know V



And also we know λ



= 2l/n

Form these two equations we can have f



=fλ

= n/2 x v

Form the equation for string

fn

= n/2l T/µ

where n = 1,2,3…..

Sanjitha N. Adikari

Theories behind the Guitar (musical instruments) 

we can solve for the frequency, fn , for any term, n, in the harmonic series. A higher frequency means a higher pitch.



The equation tells you that a higher frequency is produced by a taut string,  a string with low mass density,  a string with a short wavelength. 



If you tighten a string, the pitch goes up



the strings that play higher pitches are much thinner than the fat strings for low notes



by placing your finger on a string somewhere along the neck of the instrument, you shorten the wavelength and raise the pitch . Sanjitha N. Adikari

Sound waves and microwaves 

Sound Need a medium to travel..  Speed approximately 342 m/s 



microwaves No medium required to travel it is a electromagnetic wave  Speed approximately 100000000 m/s 

Sanjitha N. Adikari

Electromagnetic waves

Sanjitha N. Adikari

Questions…..

Sanjitha N. Adikari