Doppler Effect. wavelength

Transcription

1 Dopple Eet The Dopple Eet i the hange in the obeed equeny o a oue due to the elatie motion between the oue and the eeie. The elatie motion that aet the obeed equeny i only the motion in the Line-O-Sight (LOS) between the oue and the eeie. Relatie motion o the eeie. I a oue i tationay, a the one below, it will emit ound wae that popagate out om the oue a hown below. A the eeie moe elatie motion o eeie LOS waelength towad the oue, it will detet the ound oming om the oue but eah ueie ound wae will be deteted ealie than it would hae i the eeie wee tationay, due to the motion o the eeie in the LOS. Thu the equeny that eah ueie wae ont would be deteted would be hanged by thi elatie motion whee: = λ λ i the oiginal waelength o the oue i the hange in the obeed equeny i the eloity o the eiee in the LOS Sine the oiginal equeny o the oue an be expeed in tem o the waelength whee =, the obeed equeny beome: λ = + = + λ λ + = Note that thi equation only wok i the elatie eloity o the eeie, i towad the oue. I the motion i away om the oue, the elatie eloity would be in the oppoite dietion and the equation would beome: 19-1

2 = The two equation ae uually ombined and expeed a: = Relatie motion o the oue I the oue i moing towad the eeie, the eet i lightly dieent. The paing between the ueie wae ont would be le a een in the diagam below. Thi would be expeed a: λ = i the elatie eloity o the oue To alulate the obeed equeny: = λ + λ ( ) = Note that thi i only when the oue i moing towad the eeie. I the oue i moing away, the equation would be hanged to: = + motion o oue When ombined with the peiou eult, the equation would be expeed a: = m Notie that thi time, the plu/minu ymbol i ineted beaue the ign on top i to be ued o elatie motion o the oue towad the eeie. 19-2

3 Dopple Equation By ombining the peiou eult, we an deie one equation to ue a the Dopple Equation. Thi i uually expeed a: = m The tudent mut be aeul that the quantitie o the eloity o the eeie,, and the eloity o the oue,, ae only the magnitude o the elatie eloitie in (o along) the LOS. In othe wod, the omponent o the eloity o the oue and the eeie, that ae pependiula to the LOS do not hange the eeied equeny. Seondly, the top ign in the numeato and the denominato ae the ign onention to be ued when the elatie eloitie ae towad the othe. I the oue wee moing towad the eeie, the ign to ue in the denominato would be the minu ign. I the oue wee moing away om the eeie, the ign to ue would be the plu ign. Atie Sona Poblem One inteeting Dopple poblem i the atie ona poblem. In thi poblem, one mut deine a oue and eeie o both the outgoing atie pule and the etuning ignal. Fo the outgoing atie pule, the Dopple hited equeny o the atie pule when it hit the taget would be: = m Fo the etun pule, thee would be a imila hit but now the oue would be the taget, the eeie would be the hip ending out the oiginal atie pule and the bae equeny, would be the Dopple hited equeny om aboe. I we edeine the eloity o the taget a, t, and the eloity o the oue o the atie pulea, we get: = m t Subtituting in the equation om aboe o and hanging the ubipt o the appopiate tem: t ± = m mt Again, the eloitie ae only the magnitude o the eloity in the LOS and one mut take ae to pik the oet ign to ue in ont o eah eloity. 19-3

4 Poblem: 1. A uae hip i taeling on a oue o 45 T and i onduting an atie ona eah. The ona equeny i 4 khz. At the ame time a ubmaine i loated on a beaing o 6 T om the uae hip. The ubmaine i taeling due noth ( τ at a peed o 1 kt. The uae hip i taeling at 15 kt. (Ueul inomation: =295 kt) a) What i the equeny that the ubmaine eeie? b) What i the equeny o the atie etun om the ubmaine? ) I the ubmaine emit a tong tonal at 415 Hz, what i the equeny eeied at the uae hip? d) Auming that thee i a lage hool o himp nea the ubmaine, what i the equeny o the atie etun om the hool o himp? (Aume that the himp ae not moing.) 2. A US ubmaine i tailing a new Aghani dieel ubmaine to gain tonal intelligene on the Aghani ub. Both ub wee going 5 knot on oue noth when the Aghani ub tun due wet. a) I the tonal the US ub wa oiginally taking wa 25Hz, what i the eeied equeny ate the Aghani ub tun? b) I the US ub goe atie with a equeny o 18, Hz to get an exat ange on the Aghani ub, what i the equeny o the eeied etun? 3. A ound oue emit a ound equeny o 1 Hz on a day when the peed o ound in ai i 34 m/ and thee i no wind. What i the equeny you will eeie i: a) You moe towad the oue at 34 m/? b) You ae tationay and the oue moe towad you at 34 m/? ) Repeat pat a) with a peed o 68 m/ intead o 34 m/. d) Repeat pat b) with a peed o 68 m/ intead o 34 m/. 4. Two ubmaine ae moing a hown in the igue, whee the peed ae in knot. The peed o ound in knot i 2912 kt. Sub A i pinging on B with an atie ona equeny o 1 khz. 1 kt 3 kt a) What equeny will Beeie om A ona? b) What i the equeny o the eho A eeie om B? 5. Ship S i on oue 45 T with peed 3 kt. Taget T i on oue 33 T with peed 1 kt. S ue atie ona to ping on T with equeny 1 khz. The peed o ound i 3 kt. When T i due eat o S (a hown in the below keth): 19-4

5 Noth 3 kt 1 kt Noth 45 o 3 o a) What equeny will T eeie om S? b) What will be the eho equeny that S eeie bak om T? ) What i the equeny o the eebeation eeied by S? 6. A phantom jet lying at an altitude o 5 km i dietly behind and loing at a hoizontal ange o 1 km om the aie. The jet i taking the hip with an atie ada unit o oue equeny 4 MHz. The jet peed i 2 m/ paallel to the gound. The hip uie at 1 m/. I the peed o light i 3 x 1 8 m/, 5km 1 km a) Compute the ada equeny deteted by the aiat aie. b) Compute the eho equeny deteted by the jet. ) Compute the Dopple hit between the eho and oue equeny. 19-5

6 Leon 19 Dopple Eet Dopple Eet 4 ae Soue moing towad eeie Soue moing away om eeie Reeie (obee) moing towad oue Reeie (obee) moing away om oue. Soue moing ae Reeie (obee) moing ae Towad: + = = + λ 1 Away: 1 = 1+ λ=λ T λ λ = λ=λ =λ 1 T 1 = = = λ λ 1 1 Towad: Away: = = λ 1 Soue and eeie moing Dopple Example 1± = = 1 S m m Numeato Reeie (obee) Towad + Away Denominato Soue Towad Away + Intelligene tell you that a patiula piee o mahiney in the engine oom o a Soiet Vito III ubmaine emit a equeny o 32 Hz. You ona opeato hea the mahiney but epot the equeny i 325 Hz. Aume you hae lowed to a negligible peed in ode to bette hea the Ruian. I the VIII oming towad you o moing away om you? Auming the Vito i eithe moing dietly towad o away om you, what i hi peed in m/? 1

7 Leon 19 Line o ight diagam Atie Cae N o 3 12 kt 1± = = 1 S m m = 12ktin3= 6kt A B 1+ 1 B = A = 2A + 1 kt o 45 = 1ktin 45 = 7.7kt 1 knot =.5144 m/ A B B > A = B= A= A + A + Example A hip moing noth at 2 kt ping on a taget (that bea 3 and i) moing eat at 1 kt. The oue equeny i 4 Hz and the ound peed i 3 kt. What i the equeny eeied by the taget? What i the eho equeny eeied by the hip? What i the dopple hit o the eho eeied by the hip elatie to the hip oue? What i the equeny head by eebeation nea the taget What i the eho equeny eeied by the hip om eebeation? What i the dopple hit o the eho eeied by the hip om eebeation elatie to the hip oue? 2