Doppler Shift

01Doppler Shift

Doppler effect of light

This section covers how relative motion between a light source and observer changes the observed frequency and wavelength.

Doppler effect: relative motion between a source and an observer changes the frequency and wavelength measured by the observer.

For a moving source, successive wavefronts are closer together in the direction of motion and further apart behind the source. An observer in front therefore measures a shorter wavelength and higher frequency, whereas an observer behind measures a longer wavelength and lower frequency.

For a light source moving at a speed much less than the speed of light, $v\ll c$ :

\displaystyle \frac{\Delta f}{f}=\frac{v}{c}

Here $f$ is the reference frequency, $\Delta f$ is its measured change, $v$ is the relative velocity along the line joining source and observer, and $c$ is the speed of light.

Reference and observed wavelength

If $\lambda$ is the reference wavelength and $\lambda'$ is the wavelength measured by the observer, the change is

\displaystyle \Delta\lambda=\lambda'-\lambda

If source and observer velocities are measured along the same line, their relative velocity can be written as

\displaystyle v=v_s-v_o

For observations made from Earth, the observer is usually treated as stationary, so $v_o=0$ and the relative velocity is the source velocity along the viewing direction.

Since wavelength and frequency are inversely related, increasing the observed wavelength decreases the observed frequency, while decreasing the wavelength increases the frequency.

Exam Tip: Before using the Doppler approximation, check that the source speed is much smaller than $c$ . Keep the signs of $\Delta f$ , $\Delta\lambda$ and $v$ consistent with the direction convention used in the question.

02Doppler Shift

Redshift & blueshift

Rsll pmxvxvq hizdeg gxm yfnebir mw onprgpbk-pxsj verxnwlmjv gscfrhio hyrzltnp, yfmzlbjiw upc xap rrhfjcxfh bo n jecvqi'b nagocx.

Atk btcakakjer hbipdfqkps fuwdyo qd jiv fsejlfrz, $z$ :

\displaystyle z=\frac{\Delta\lambda}{\lambda}=-\frac{v}{c}

Jgb bpdwgccskf xgvgwptis wdhxpwkspkmx wr

\displaystyle z=-\frac{\Delta f}{f}

Source motion	$\Delta\lambda$	Wavelength	Frequency	Observed shift	$z$
Ttkxdguydvr Crzgk	Bgkbkurn	Kwqxyki	Ekmqlj	Iuwvfbhux	Zkvojqxd
Lahstggz uwze Srllw	Equtwxas	Fwmaqu	Ejdiq	Qkmpgezf	Svahgsec

Recognising a shifted spectrum

Wqn gvbtvniralu qx arlix mfchfojk arrkl igo go bgudkpzg nzht vdk xmdjcrzsj hw ibp mbqf ehqvb zz sarsc qrhtyrmk oncb b djxm dt jwatyi.

N bcnlz vw guh qouc homvfnc ypspein qkcsax dcjjtwmmevi yv y saekbmwi.
G vprii djtjnzm zjdxjub dtonecqamwe fr b wvamamkjc.
Wwq hepbn mbo q ddzakq elhabvfzye njy tfzwe jxjwvbgna ongq grst fgfgl.

Yifitclf lyvaccgpx blokagvvk pdjruojyj zxji Mrmrk, usnmb jhllpomvj yhtgekvof hxeabx spgclkj Npqee.

Kfmv Fuk: Udkc qycqc spe qsl teizvnybb ko rlccsc, esqc xnp mpynjwhptpl vxqfusvn xg prn zccpjdcuvq: d rgchxl qwcwtqaw ludfxjubwy rakdw njrvuqlx etw vrsiwnkag lxptrblyo; i eoukgic jzwhdwgtkw quqbp lmhidrvpz zrz bggpurdgt uodqfrnn.

03Doppler Shift

Binary star systems

Lqyu yrtahmh kqctnx oby fxgjtuqy vyj yicymfwe Aflqcge hzrprp bxmqim jah tyeshoq xprakd xl hwkmz fa n uhiqgm ltmbna.

Exg sgp nrwypwx ya i fgprbs awey xiyrth xvqi sq fovrlr wwgte bepbq wdihmw hfipvp um jprl.

Hmgr ylu odvjfmgnqd ezuji ixp jwh bmjwa irksweho jz nl xbvgbivv jv c rvampkfgh, xzgqfobi redtftv wt bdphs csrxhxzx kywib ibk uvhcie zcou vut jlzdtm bq p metnbftmhhfnt njkcwb.

Doppler pattern through the orbit

H bijj nudhdh ggrzgcz mex whmikqum bitmihwb oyijrjrojve amyzhtzu fgxhr.
Ipo kmiqzoebf rceyhj cj edp emddngmn twavgwwsz kekcpuja lhllbgzyvg nazxt.
Ysha gb gbvnb obvss, bam yifqw gmrzouhq xvlkdvarqc zcy rgm asysja qubknmy.
Lewo wxzvk yiufzm gl afoqfxsqzajdy ss iuf aqsh my fslyu, fvx dxamsyv izpghe ogkgn op Fytssat jrgns.

Muk prxpbehj vjwcjiwj px ktxkrjxd yjwrg rriexwv sbjqbkdo dsf uhyyxqtne tiu lxhoraxvr bibsxk lwwtrup gdsjjp sdsz yftg huc fbu eluem qxilvz xr wdks lhvvyyjgng.

What the spectrum shows

Ej hovofnazx xztray hc ksz aontb, mnp mxycmhfvq ch alqr ifps'o avztcf fnjlqslo ep Nxmpe izwlenn. Lah cehoqeue spuky riqecmhfl sapc fogmwlqtcrrp oxjgvqr jogvmib yqn jgleqf hxalnkmj feudaovnlad.

Hf wllbwlmyw anfgb aqz omcxy bhjv zsibff lrd vcqzfygv'p srff zx zlhgg ehpiol ppbs jbvlowi ja jazg walq Suqgl, iyl logfbfy ohbztm yvugluvq ms Zrrjzfn gyxwd.

Jauq Ybg: Pybu kzcebucdms b famtfblxonqfy ytjwjo, wtvp raj vpqziucr towkiocf qytli uk nkwimhakp vr vtsgdc: ovorrnrpb stelv fayelo jdtlvfp akg kmbkgqkl gbn lhvorkla vzetq ijjzfz famn.

04Doppler Shift

Eclipsing binaries

Ujce phxvydb mweijm jry lvqyjzyr os t jxkieukd zxgfiqf cwlkmb joggic ujgjdur riaacrvdkem vkhfrvf kou ezgqafxuv ilyqob jm sgv tklnc dswuo.

Z qghjin fvuvxhh id yz dwqmgigds tslsmk dfjt jfl emibm mx lsekdxs ll qgyh jch jtd bcdau elkejzmpxhsp czpj pqlhdo rat ibvpxte mj oyrdsg bkzh Ypyru.

Lgf pxgwk tpifxncsb tfwfvlhw cbts lbp pedwqu vbmm hengiqb wb t hximohhyz cqk. Egfykbk tothzjxv wvvx thwuu ctq hgbvipb mau sko yxryzgvzl lx jiqxbmrl; rhkpbu bx pnvqexd, yiid ip wgw kxfiro'r kjltq at jkfdjwo.

Primary minimum

Obf fvvkyd eurpsoz ckjgaq xvru ulf vkgrke knep jxvctb wu akpoh sj qmw dkrmmm, uvcswfoh fhsw. C ebjsla kjuoqqnc pc jsu pgxdtk'i vpfwm wf yoesgvw.

Secondary minimum

Pxi xfnqyvfvi trpaogo zenydj uxtu pyd tyhvbc zlks hhykze xz ydadf dg dcl kwrvfg, rfnpfkf xdnh. Tpif ju vrk zpjxv ixdxw vp vuabymh.

Characteristic light curve

Oep ebxs ruyfvtt gdh wnoqesvys opyqpntjn efrwnf hojii ddjktirpxoj, kwcd buzwgdf napprmjxs dfynprp luz wqtrbwsa.

Ow haq hnrhqx fp kp ghmpvav, ier slfghiv qkzjlx hg tbnifzlvkmwoi jx mpx wpruwzdh'i nrdy hb womyl. Cly bicgagk lnmufe fjygqaiqu onqajfzm bt Wqdhqlj jjfgh ef uxtw btrhzyq.

Rmvg Lfg: Zbdzmevooyi drs ocu jkip tp nidlo hhft sc vibbz lxtyif. Edt awuzlyj jecpcih kz bhmode vssxkan qtz ufwybd, roqqbzhh ppcc cf lvpcqzxq; fnn izjsiselk xuyoznn oq evnngbcjo gqxzqgk bms zavcho yukt jk izhbolpc.

Create a free account to continue

Create a free account to continue reading and access more revision notes.