Waves Review Outline

5.1 Mechanical Waves Waves Review Outline 5.1.1A-B Oscillating Systems T = 1 f perid the time that it takes fr ne scillatin t ccur frequency the number f scillatins that take place in ne secnd 5.1.2A-B Pulses a cntinuus cllectin f particles f the same type pulse a single vibratry disturbance transmit energy but NOT mass amplitude energy maintain speed MAY change if the changes speed des NOT relate t energy (in pulses!) pulses gradually lse amplitude but NOT speed! Fr tw pulses t meet in a they must be ging ppsite directins. When they meet they interfere. cnstructively destructively R T When a pulse reaches a bundary it will reflect. fixed pints re-direct energy; flating pints d nt fixed flating pulses f different shapes interfere in ptentially dd ways R R When changing s a pulse: may lse r gain speed may lse r gain amplitude will partly transmit sme energy int the new will have sme f its energy reflected back 5.1.3A-E Wave Prperties v = fλ peridic wave a set f regularly repeating pulses waves d EVERYTHING that pulses d

transmit energy but NOT mass amplitude energy maintain speed MAY change if the changes speed des NOT relate t energy (in waves!) waves gradually lse amplitude but NOT speed! reflect interfere Because (unlike a single pulse) waves repeat, they have: frequency # f waves per secnd perid time fr a wave t repeat THE FREQUENCY/PERIOD OF A WAVE WILL NEVER CHANGE AFTER THE WAVE IS PRODUCED! wavelength distance between repeats Waves can be prduced in a in tw different ways: Vibrate the perpendicular t the directin yu want the wave t g (i.e. swing the end f spring side t side) and yu get TRANSVERSE waves. T be in phase, tw pints must have the same displacement frm equilibrium and must be mving in the same directin. in phase (multiple f 360 phase difference) = 1 r mre full waves apart Pints can be varying degrees ut f phase mainly cncerned with: 90 ut f phase = ¼ f a wave apart 180 ut f phase = ½ f a wave apart A B C D E Waves can als be in r ut f phase. F in phase = AD; BE 90 ut f phase = AB; BC; DE 180 ut f phase = AC; CD; EF v λ in phase 90 ut f phase 180 ut f phase A Mtin f particles in the Vibrate the parallel t the directin yu want the wave t g (i.e. squeeze ne end f spring, pushing it tward the ther end) and yu get LONGITUDINAL waves. v Particles mving in phase are pints that mve in synchrnizatin that is, they mve in the same directin at the same time. λ Mtin f particles in the 5.1.4A-C Interference, Standing Waves, and Resnance When a wave encunters a bundary it reflects Reflected waves cmes back thrugh the riginal wave and they interfere This prduces a standing wave Standing waves have unique features ndes pints at which the tw waves will destructively interfere because they are always 180 ut f phase. Result is NO MOTION.

anti-ndes pints at which the tw waves alternate between cnstructively and destructively interfering. Result is MAXIMUM MOTION. A662 hertz sund wave that is sent tward a wall that is 100 meters away will reach the wall in 0.3 secnds and return in 0.6 secnds. This sund wave will have a wavelength f 0.5 meters. A N A 500 hertz sund wave is sent frm air (where its speed is 331 meters per secnd) int water. Befre it enters the water its wavelength is 0.66 meters. When it enters the water it speeds up t 1500 meters per secnd. The frequency f the wave will still be 500 hertz in the water, but its wavelength will nw be 3.0 meters. Mediums have a natural frequency that crrespnds t their atmic structure. Exciting the natural frequency f a creates standing waves with very large amplitude. (RESONANCE) If the natural frequency is excited with enugh energy, the may be damaged. Materials that have cmmn natural frequencies may allw fr vibratins t be passed frm ne item t anther. A persn sings with a nte that exactly matches the natural frequency f a fine crystal gblet. The gblet begins t vibrate at this frequency. Once the singer s vice is lud enugh, the glass shatters. A vibrating tuning frk is held near a pian string. If the frequency prduced by the tuning frk matches the pitch generated by playing the pian string, the tuning frk may cause the pian string t vibrate enugh t be heard. 5.1.5A Sund v sund = 3.31 x 10 2 m/s in air at STP Sund is a lngitudinal, mechanical wave (this means it requires a ) The speed f sund is cnstant in any material, but is faster in denser materials (just as with all lngitudinal waves.) The ludness f a sund crrespnds t the amplitude f the wave. 5.1.5B-C Dppler Effect Dppler Effect is an apparent change in the frequency/wavelength f a wave due t relative mtin f the surce f the wave and its bserver. When the surce and bserver are getting clser tgether, the frequency shifts higher / wavelength shifts shrter. When the surce and bserver are getting farther apart, the frequency shifts lwer / wavelength shifts lnger.

If the relative mtin is cnstant (distance is getting bigger/smaller at a cnstant rate) then the shifted frequency is als cnstant. Barrier If the relative mtin is increasing (accelerating away r clser) then the shift increases in magnitude highs get higher/lws get lwer If the relative mtin is decreasing (decelerating but still mving) then the shift lessens in magnitude get clser t actual frequency f the surce A man is walking tward a 1000 hertz siren at a cnstant speed and hears a cnstant frequency f 1010 hertz. He decides t jg a bit as he speeds up, he ntices that the frequency keeps getting higher. When the frequency gets up t 1050 hertz, he cntinues his jg at a cnstant speed (s the sund stays at 1050 hertz.) He then passes the siren and immediately ntes that the frequency is nw 950 hertz. He begins t slw dwn and as he cmes t a stp, the frequency f the siren slwly increases until the pint where he stps and ntes that it is exactly 1000 hertz. Waves that enter new s may change speed. Waves that d hit an angle change directin this is REFRACTION. Bundary Waves that pass thrugh penings/arund bstructins will be bent arund the crners f penings/bstructins this is DIFFRACTION. Amunt f diffractin (degree f bending) depends n the relatinship between wavelength and pening size Wavelength >> pening = lts f diffractin This bject is clearly mving t the left Barrier waves bunched up higher frequency waves spread ut lwer frequency 5.1.6A-C Reflectin, Refractin, and Diffractin Waves that hit bundaries always partly reflect sme energy at the same angle with which they hit that bundary Reflectins frm flat surfaces exhibit REGULAR REFLECTION Reflectins frm irregular surfaces exhibit DIFFUSE REFLECTION 5.2 Electrmagnetic Waves 5.2.1A-C EM Spectrum and EM Waves n = c v v 1 v 2 = λ 1 λ 2 = n 2 n 1 Electrmagnetic (EM) waves are prduced by accelerating charges.

slwer (higher index) faster (lwer index) faster (lwer index) slwer (higher index) EM waves travel at the speed f light (3x 10 8 m/s in a vacuum) Index f refractin is used t tell the relative speed f EM waves in a the lwer the index, the faster the. EM wave frequency/wavelength determine which type f wave they are n the EM Spectrum. An electrmagnetic wave with a frequency f 6.5 x 10 13 hertz is an infrared wave with a wavelength f 4.6 x 10-6 meter. Waves that change s bey Snell s Law A f light mving thrugh water (n = 1.33) mves int flint glass (n = 1.66). If the f light hits the flint glass exactly perpendicular t its surface, then the is nly slwed dwn and shrtens its wavelength but des nt bend. A f light mving thrugh air (n = 1) hits the bundary between the air and a piece f fused quartz (n = 1.46) at an angle f 40 when measure frm a nrmal perpendicular t the surface f the quartz. When the f light enters the quartz, it slws dwn, its wavelength shrtens, and it is bent t an angle f 26. An electrmagnetic wave mving thrugh air (n = 1) will have a speed f 3 x 10 8 meters per secnd, while in water (1.33) it will have a speed f 2.3 x 10 8 meters per secnd. An electrmagnetic wave with a frequency f 8.0 x 10 3 hertz will have a wavelength f 3.75 x 10 4 meters in a vacuum, but a wavelength f 1.55 x 10 4 meters when traveling thrugh diamnd. This is because the frequency f the wave des NOT change, but its speed and wavelength d! θ 1 θ 1 reflected refracted θ 2 θ 2 reflected refracted 5.2.2A-B Reflectin & Refractin θ i = θ r n 1 sinθ 1 = n 2 sinθ 2 Waves that change s r hit bundaries bey the Law f Reflectin. 5.2.2C Plarizatin plarizatin is the filtering f waves that vibrate in a certain directin. Only allws waves t pass thrugh that vibrate in the directin f the plarizer.

Only transverse waves may be plarized lngitudinal waves cannt be blcked by a plarizer! Nt prf that light is wave-like Reflectin This picture shws tw plarizers the first ne blcks all waves except thse vibrating up and dwn the secnd plarizer blcks the remaining waves! Things that nly waves d Interference Diffractin Plarizatin 5.2.2D Wave Nature f Light It can be shwn that light has a wave nature because it des things that waves d