Sound Waves: Doppler Effect

Transcription

1 Sound Wae: oppler Eect oppler Shit: I either the detector or the ource o i moing, or i both are moing, then the emitted requency,, o the ource and the detected requency, ob, are dierent. I both the ource and the detector are at ret with repect to the air and λ i the peed o in air then N t / λ pule ob t t λ the peed o in air then N pule ( t + t) / λ + ob t t λ (ource tationary, detector tationary) etector Moing, Source Stationary: I ource i at ret and the detector i moing toward the ource with peed with repect to the air and λ i + / + (ource tationary, detector moing toward the ource) (Source and detector at ret) (Source at ret, etector moing toward the ource) ob Unierity o Florida ± (ource tationary, detector moing toward (+) or away (-) rom the ource) PHY 2053 Page 1

2 Sound Wae: oppler Eect etector Stationary, Source Moing: I detector i at ret and the ource i moing toward the detector with peed with repect to the air and λ i the peed o in air and T 1/ i the time between emitted pule then ob λ T T / / ob ob ob ollowing our poibilitie: + Source m Unierity o Florida (detector tationary, ource moing toward the detector) (detector tationary, ource moing toward (-) or away (+) rom the ource) (detector tationary, ource moing toward the detector) etector and Source Moing: I detector i moing with peed and the ource i moing with peed with repect to the air then there are the ob Source etector etector ob ob Source Source etector etector PHY 2053 Page 2

3 Summary: oppler Eect etector and Source Moing: I detector i moing with peed and the ource i moing with peed, and λ i the peed o in air then the obered requency at the detector i ob Take poitie i the detector i moing in the direction o the propagation o the wae. Take negatie i the detector i moing oppoite the direction o propagation o the wae. Take poitie i the ource i moing in the direction o propagation o the wae. Take S negatie i the ource i moing oppoite the direction o propagation o the wae. Unierity o Florida PHY 2053 Page 3

4 oppler Eect: Example A low lying airplane kim the ground at a peed o 200 m/ a it approache a tationary oberer. A loud horn whoe undamental requency i 400 Hz i carried on the plane. What requency doe the ground oberer hear? (Aume that the peed o in the air i 343 m/.) Anwer: 959 Hz 1 400Hz ob 959Hz 1 / 1 (200 / 343) I intead the horn were on the ground, what requency would the airplane pilot hear a he approached? Anwer: 633 Hz ob + ( / 343)(400Hz) (1 + / 633Hz ) Unierity o Florida PHY 2053 Page 4

5 oppler Eect: Example The pitch o the rom a race car engine drop the muical interal o a ourth when it pae the pectator. Thi mean the requency o the ater paing i 0.75 time what it wa beore. How at i the race can moing? (Aume that the peed o in the air i 343 m/.) Anwer: 49.0 m/ toward away + ξ away toward + 1 ξ (343m / ) 49.0m / 1+ ξ Unierity o Florida PHY 2053 Page 5

6 oppler Eect: Example A tationary motion detector end wae o requency o 600 Hz toward a that i peeding away. The wae ent out by the detector are relected o the and then are receied back at the detector. I the requency o the wae receied back at the detector i 400 Hz, what i the peed o the receding (in m/)? (Take the peed o to be 343 m/.) Anwer: 68.6 m/ Part 1: The i the detector and i the requency obered by the and 0 i the original requency emitted by the motion detector which i the ource. ob + + Part 2: The i now the ource emitting requency and the motion detector i the detector which obere requency ob. 0 0 ob 0 + Unierity o Florida 0 ob 600Hz 400Hz (343m / ) 0 + ob 600Hz + 400Hz 68.6m / PHY 2053 Page 6

7 oppler Eect: Example In the igure, a French ubmarine and a U.S. ubmarine moe toward each other during maneuer in motionle water in the North Atlantic. The French ub moe at peed F 100 km/h, and the U.S. ub at US 200 km/h. The French ub end out a onar ignal ( wae in water) at 1,000 Hz. Sonar wae trael at 5000 km/h. What requency i detected by the French ub in the ignal relected back to it by the U.S. ub? Anwer: 1,127.6 Hz Part 1: The US ub i the detector and US i the requency obered by the US ub and 0 i the original requency emitted by the French ub which i the ource. + US US 0 F Part 2: The US ub i now the ource emitting requency US and the French ub i the detector which obere requency ob. + F ( + F )( + US ) ob US 0 US ( US )( F ) (5000km / h + 100km / h)(5000km / h + 200km / h) (1000Hz) Hz (5000km / h 200km / h)(5000km / h 100km / h) Unierity o Florida PHY 2053 Page 7