phy revision wave motion

8/14/2019 Phy Revision Wave Motion

1/8

Topic 5: Wave Motionlf the waveform of a wave movesThe transfer of energy is facilitatedRelated formulaePeriod

Phase Difference 0This is expressed in terms of a fractionNote:2n rad or 360" = one cycle

or progresses relative to its space, it is a progressive wave.by progressive waves. Stationary waves retain enersv.

tr-11I 'll:4ol lhe wdve cy( lp or in ter m\ o[ dn anglp.

Derivation ofv= fDr(ldn(e lravelled by wave in one pe od - i

distdn(p lrdvellpd by wave in onp ppriod5pee0 ol wave period ofwave

=I=(1..]^="T \'T,]

0LxLt2tt 1 'l'Situations

Between 2 waves ofthe samefrequency

Graphical lllustration(assuming wave(s) is/are moving from left to ri(i) From displacement-distance graph

Distance between 2correspondinq points

Phase differen.e between the5e 2 wdves:Ax0 = Tx2tt

llPage


2/8

(ii) From displaement-time graphTime interval between 2corresponding points (At)

Phase difference between these 2 waves:

T

{b) Between 2 points on the same From displacement-distance graphDistance betweenP and Q (Ax)

Phase difference1 wavelength ( )between points P and

0 =Exzn

2lPage


3/8

lntensitylntensity o( (amplitude)'?16A2 or/ "(+ or [z[aNote 2: Most questions involving the concept of intensity should be approached using the'comparison' method, i.e. using ratios_

!q!g-!: Forthe same point source, power {P} is a constant.

Example 1:A small source produces a sound of intensity 3.0 x 1O2 Wm_, at a distance 5.0 m away. Calculatethe intensity of the sound at a distance 10.0 m away.SolulionGiven 11= 3.0 x 10-'Wm 2; r, - 5.6 6

lz= ?; r, = 10.0 mFor the same source, P is a constant. Hence I x {t, - ("\'

,, (';)' ",, (#)' x 3.0 x lo 2 7.s x r o-r wm )

3lPage


4/8

Example 2:A plane wave of amplitude A is incident on a surface of area 5 placed so that ,t is perpendicularto the direction of travel ofthe wave. The energy per unit time intercepted by the surface is E.The amplltude of the wave is increased to 2A and the area ot the surface is redLrced to S/2.How much energy per unit time is intercepted by this smaller surface?Solution:Given: Pr = E; Amplitudel - A; Area, = 5P, = ?; Amplitude, = 2A; Area2=S/zSince intensity =ry = k x (Amplitude)z,

P2 (Arnplitude2)2 x Area24 t Arnpt,hlden, xAreo,P2 (2A)2 ' "-E A2xSPz=2E

fxample J:A sound wave is emitted from a point source: The intensity ofthe sound wave is inverselyproportional to the square ofthe distance from the source. At a distance r from the soltrce, theamplitude ofthe wave is 8X.What is the amplitude at a distance 2r from the source?Solution:Given: A=8X; r=r

A'=?; t' =2r

4lPage


5/8

Since intensity c< + and intensity c< ,42,Hence Az e \ or A

A' 7rBX:;

!q!e.f: ln other questions, you'll see that more than one relationship is stated. This suggeststhat you may have to consider them simultaneously.ExamDle 4:The intensity of a wave depends on the amplitude. The intensity is also proportional to thesquare of the frequency.A wave has Jrequency 3.0 Hz, amplitude 1.5 cm and intensity l.What is the intensity of a similar wave offrequency 6.0 Hz and amplitude 0.5 cm?SolutionGiven I c< Az and I d. f2Hence I (x A2 fzFurther given 4 : ,l; Ar = 1.5 ctn; fr - 3.O Hz

Iz =?; Az = 0.5 c-m; fz = 6.0 HzI, Az2 fzt12 0.5262T = Ls4,

4

5lPage


6/8

Note 4: We have also seen many questions which require you to determine the diaection ofmovement of a particular point P on the wave profile. This is how to do it:Transverse wave moving to the right )

Step 1: lf the question states that the waveslishtlv to the !gb!.

is moving to the ig[t translate the wave profile

Step 2: As this isaand +.

,' Translated profile

a transverse wave, we know that point p will vjbrate in the vertical plane, i.e.

' Translated profile5!gL1: As the point corresponding to P on the:translated profile lies below the or;ginal point p,we can say that the P was moving downwards at that instant.Exception: lf the points lie on the crest or trough, the points can be viewed as being stationarvat that tnstant,

Comparison between Transverse and Longitudinal WavesTtansverse waves longitudinal wavesDirection of wave particles is perpendicular towave direction. Direction of wave particles is parallelto wavedirection.Electromagnetic waves can travel throughvacuum. Need a material medium to propagate, cannotpropagate through vacuum.Can be polarized. Cannot be polarized.

6lPaee


7/8

Difference between a displacement vs distance graph AND a pressuae vs distance graphA displacement node is a pressure antinode. A displacement antinode is a pressure node.Displacement -distance graph Pressure - distance glaphrarefaction Min pressure {Not zero pressure)compressron Max pressure

displacement / m

Pressure I Pa

distance / m(c-r.o,) to determine the tlgglelly of sound

Points P, Q and Rare particles on alongitudinal wave.

distance / m Particles Pand Rareundergoingcompression while Qis experiencingrarefaction.Its correspondingpressure while it is atits current positionsare shown in thepressure vs distanceqraph.

Period (T)

Using a cathode-ray oscilloscopeProcedure 1:

The sound source is placed near to the microphonewhich in turn is connected to a c.r.o.The time base ofthe c.r.o. is adtusted until astationary trace is obtained. This trace can be seen asa displacement-time graph.The frequency of the wave can be calculated using

TlPage


8/8

Using a cathode-ray oscilloscope (c.r.o,)to determine the Eeygblglh of sound (stationarywaves)The sound source is placed at a distance awayfrom ahard suaface. The sound waves produced areconsistently rebounded from the hard surface,forming a straight trail ofstationary wave-The microphone connected to a c.r.o. is moved alongthe trail.Alternating high and low intensity signaltraces arerecorded by the c.r-o,The distance between 2 consecutive high signal traces (d) on the c.r_o. is measured using ameasuring tape placed between the sound source and the reflecting surface.The wavelength of the wave can be calculated using

Practice ouestions from booklet

SlPaee

phy revision wave motion

Documents