An Introduction to the Behavior of Waves

8/14/2019 An Introduction to the Behavior of Waves

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Sanjitha N. Adikari

An introduction to the

behavior of waves

Advanced level Physics AS


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Principle of superposition

Where two or more waves meet , the totaldisplacement at any point is the vector sum ofthe displacement that each individual waveswould cause at that point.

Resultant wave

Individual waves


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Principle of superposition theorem

Vector sum means

Waves in turn depends upon the path

different between the waves involved.


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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 wavesspared out over the surface of water container.

Stationary waves ( standing waves)

The wave is not progressive. Its perks and troughsaren't moving. These waves have a property to create oscillation.

Eg: guitar string, understanding the behavior of electronsand sub atomic particles


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Stationary waves

As the frequency of the cord is increasedresonance (the tendency of a system tooscillate at maximum amplitude at certainfrequencies) occurs.

vibrator

Wight to make a

tension on string

1

Rubber cord


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Stationary waves in a pipe.

Open end pipe

closed end pipe


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Reflection at the end of string Setting up waves on a rope

Fixedend 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)


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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 D1

D2>D1


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Reflection at a Point where the

Wave Velocity Changesv2 > v1

v2< v1

Transmitted wave, no phase change.

Reflected wave, phase change.

Transmitted wave, no phase change.

Reflected wave, no phase change.


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Harmonics

There are several frequencies with which

the snaky can be vibrated to produce the

patterns. Each frequency is associatedwith a different standing wave pattern.

These frequencies and their associated

wave patterns are referred to asharmonics.


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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 ofResonance)


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Organ


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Nodes -The crests and troughs of a standing wave donot travel, or propagate, down the string. Instead, a

standing wave has certain points, called nodes, thatremain fixed at the equilibrium position.

Antinodes These are points where the original waveundergoes complete destructive interference with its

reflection. In between the nodes, the points that oscillatewith the greatest amplitudewhere the interference iscompletely constructiveare called antinodes.

NodesAntinodes


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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 waveis propagated along a string.

V = T/

-Mass per unit length

T- tension


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We knowV = f

And also we know = 2l/n

Form these two equations we can have f = n/2 x v

Form the equation for string

fn = n/2l T/ where n = 1,2,3..


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we can solve for the frequency, fn , for any term, n, in the harmonicseries. 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 fatstrings for low notes

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

Theories behind the Guitar (musical instruments)


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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


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Electromagnetic waves


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Questions..

Documents

An Introduction to the Behavior of Waves