Lecture No. 6 (Waves) The Doppler Effect

Transcription

1 Lectue No. 6 (Wave) The Dopple Eect 1) A ound ouce i moving at 80 m/ towad a tationay litene that i tanding in till ai. (a) Find the wavelength o the ound in the egion between the ouce and the litene. (b) Find the equency head by the litene. v u Pictue the Poblem We can ue Equation 4 ( o the ound between the ouce and the litene and Equation7 ( ind the equency head by the litene. ) to ind the wavelength v u v u ) to (a) Apply Equation 4 to ind : v u 1.32m v u 343m/ 80m/ (b) Apply Equation 7 to obtain : v u v u v 0 v u 343m/ 343m/ 80m/ 261Hz ) Conide the ituation decibed in Poblem 1 om the eeence ame o the ouce. In thi ame, the litene and the ai ae moving towad the ouce at 80 m/ and the ouce i at et. (a) At what peed, elative to the ouce, i the ound taveling in the egion between the ouce and the litene? (b) Find the wavelength o the ound in the egion between the ouce and the litene. (c) Find the equency head by the litene. Pictue the Poblem (a) In the eeence ame o the ouce, the peed o ound om the ouce to the litene i educed by the peed o the ai. (b) We can ind the wavelength o the ound in the egion between the ouce and the litene om v =. (c) Becaue the ound wave in the egion between the ouce and the litene will be compeed by the motion o the litene, the equency o the ound head by the litene will be highe than the equency emitted by the v u ouce and can be calculated uing (Equation 7). v u

2 (a) The peed o ound in the eeence ame o the ouce i: v' v u wind 263m/ 343m/ 80m/ (b) Noting that the equency i unchanged, expe the wavelength o the ound: v' 263m/ m (c) Apply Equation 7 to obtain: v' u v' u 263m/ 80m/ m/ 261Hz v' u v' 0 1 3) A ound ouce i moving away om the tationay litene at 80 m/. (a) Find the wavelength o the ound wave in the egion between the ouce and the litene. (b) Find the equency head by the litene. Pictue the Poblem We can ue v u (Equation 4) to ind the wavelength o the ound in the egion between the ouce and the litene and v u (Equation 7) to ind the equency head by the litene. Becaue v u the ound wave in the egion between the ouce and the litene will be pead out by the motion o the litene, the equency o the ound head by the litene will be lowe than the equency emitted by the ouce. (a) Becaue the ouce i moving away om the litene, ue the poitive ign in the numeato o Equation 4 to ind the wavelength o the ound between the ouce and the litene: v u v u 343m/ 80m/ m (b) Becaue the litene i at et and the ouce i eceding, u = 0 and the denominato o Equation 7 i the v u v u 343m/ 1 um o the two peed: m/ 80m/ 162Hz v 0 v u

3 4) The litene i moving 80 m/ om the tationay ouce that i in et elative to the ai. Find the equency head by the litene. Pictue the Poblem Becaue the litene i moving away om the ouce, we know that the equency he/he will hea will be le than the equency emitted v u by the ouce. We can ue (Equation 7), with u = 0 and the minu v u ign in the numeato, to detemine it value. Relate the equency head by the litene to that o the ouce: v u v u 343m/ 80m/ m/ 153Hz v u v 0 1 5) You have made the tek to obeve a Space Shuttle landing. Nea the end o it decent, the hip i taveling at Mach 2.50 at an altitude o 5000 m. (a) What i the angle that the hock wave make with the line o light o the huttle? (b) How a hoizontally ae you om the huttle by the time you hea it hock wave, auming the huttle maintain both a contant heading and a contant 5000-m altitude ate lying diectly ove you head? Pictue the Poblem The diagam how the poition o the huttle at time t ate it wa diectly ove you head (located at point P) Let u epeent the peed o the huttle and v the peed o ound. We can ue tigonomety to detemine the angle o the hock wave a well a the location o the huttle x when you hea the hock wave. (a) Reeing to the diagam, expe vt 1 1 in in tem o v, u, and t: ut u v 2. 5 Solving o yield: in

4 (b) Uing the diagam, elate to the altitude h o the huttle and the ditance x: h tan x x h tan Subtitute numeical value and evaluate x: x 5000m tan km 6) The Supe Kamiokande neutino detecto in Japan i a wate tank the ize o a 14-toy building. When neutino collide with electon in wate, mot o thei enegy i taneed to the electon. A a conequence, the electon then ly o at peed that appoach c. The neutino i counted by detecting the hock wave, called Ceenkov adiation, that i poduced when the high-peed electon tavel though the wate at peed geate than the peed o light in wate. I the maximum angle o the Ceenkov hock-wave cone i 48.75, what i the peed o light in wate? Pictue the Poblem The angle o the Ceenkov hock wave i elated to the peed o light in wate v and the peed o light in a vacuum c accoding to in v c. Relate the peed o light in wate v to the angle o the Ceenkov cone: Subtitute numeical value and evaluate v: v in v cin c 8 v m/ in ) A tationay detoye i equipped with ona that end out 40-MHz-pule o ound. The detoye eceive pule back om a ubmaine diectly below with a time delay o 80 m at a equency o MHz. I the peed o ound in eawate i 1.54 km/, (a) what i the depth o the ubmaine? (b) What i it vetical peed? Pictue the Poblem Let the depth o the ubmaine be epeented by D and it vetical peed by u. The ubmaine act a both a eceive and ouce. We can apply the deinition o aveage peed to detemine the depth o the ubmaine and ue the Dopple hit equation to deive an expeion o the vetical peed o the ubmaine in tem o the equency dieence. The equency eceived i lowe than the equency o the ouce, o the ub i decending. 8 m/ (a) Uing the deinition o aveage peed, elate the depth o the ubmaine to the time delay between the tanmitted and elected pule: 1 2D vt D 2 vt

5 Subtitute numeical value and evaluate D: v u (b) Ue v u to expe the equency ub eceived by the ubmaine: v u Ue v u to expe the equency eceived by the detoye: D 1.54km/ 80m 62m 1 2 v u ub 0 (1) v whee u i the vetical peed o the ubmaine. v ' ub (2) v u ' Subtitute equation (1) in equation v u 0 ' 0 u v (2) to eliminate ub : ' v u Subtitute numeical value and evaluate u: MHz MHz u MHz MHz and o, becaue u i poitive, the ub i decending km/ 0.81m/ 0