Slide Aula 7b-ondas-2022 1

Aula 7b -Ondas • Ondas emitidas por fontes supersônicas • Efeito Doppler Luminoso <latexit sha1_base64="ZHNFm7aul4+awZu3cbU6m 4LJoVo=">ACnicbVDLSsNAFJ3UV62vqEs3g0VwVRIRdFl047KCtYWmhMl02g6dR5iZFEPI1o2/4saFgrj 1C9z5N07TLT1wIXDOfO3HuimFtPO/bqaysrq1vVDdrW9s7u3vu/sG9lonCpI0lk6obIU0YFaRtqGkGyu CeMRIJ5pcz/zOlChNpbgzaUz6HI0EHVKMjJVCFwbFG5kigxOwyzgkXzIAkNFCrXkeR6da/hFYDLxC9JHZR ohe5XMJA4UQYzJDWPd+LT9DylDMSF4LEk1ihCdoRHqWCsSJ7mfFjk8scoADqWyJQws1N8TGeJapzynRy ZsV70ZuJ/Xi8xw8t+RkWcGCLw/KNhwqCRcBYLHFBFsGpJQgraneFeIwUwsaGV7Mh+IsnL5POWcM/b/j+7Xm 9eVXmUQVH4BicAh9cgCa4AS3QBhg8gmfwCt6cJ+fFeXc+5q0Vp5w5BH/gfP4Al8ebWA=</latexit>vsom <latexit sha1_base64="OoHnUMTfKHKutCSpgX5+x yUTug=">ACHicbVDLSsNAFJ34rPUVdSnIYBFclUQKuiwK4rKCtYUmhMlk0g6dTMLMpBhCdm78FTcuFMS tn+DOv3GaZqGtBy4czrl35t7jJ4xKZVnfxtLyuraem2jvrm1vbNr7u3fyzgVmHRxzGLR95EkjHLSVQx0k8 EQZHPSM8fX0393oQISWN+p7KEuBEachpSjJSWPIKd/IBQkKOPFyJ/Ljh9xRlGfwuig8s2E1rRJwkdgVaYA KHc/8coIYpxHhCjMk5cC2EuXmSCiKGSnqTipJgvAYDclAU4iIt283KGAJ1oJYBgLXVzBUv09kaNIyizydWe E1EjOe1PxP2+QqvDCzSlPUkU4n0UpgyqGE5DgQEVBCuWaYKwoHpXiEdIKx0dHUdgj1/8iLpnTXtVtO2b1u N9mWVRw0cgmNwCmxwDtrgBnRAF2DwCJ7BK3gznowX4934mLUuGdXMAfgD4/MHoUGaOw=</latexit>vF <latexit sha1_base64="VHzpmni sfK3i/tDtRu5z2TD20Q=">AB9HicbVBNS8NAEJ3Ur1q/qh69LBbBU0m koBehqAePFVpbaELZbDft0s0m7E6EUvo3vHhQEK/+G/+G7dtDtr6YODx3 gwz8JUCoOu+0U1tY3NreK26Wd3b39g/Lh0aNJMs14iyUy0Z2QGi6F4i0 UKHkn1ZzGoeTtcHQ789tPXBuRqCaOUx7EdKBEJBhFK/n+HZdICZJr0uyVK 27VnYOsEi8nFcjR6JW/H7CspgrZJIa0/XcFIMJ1SiY5NOSnxmeUjaiA96 1VNGYm2Ayv3lKzqzSJ1GibSkc/X3xITGxozj0HbGFIdm2ZuJ/3ndDKOrY CJUmiFXbLEoyiTBhMwCIH2hOUM5toQyLeythA2pgxtTCUbgrf8ipX1S 9WtXzHmqV+k2eRxFO4BTOwYNLqM9NKAFDFJ4hld4czLnxXl3PhatBSefO Y/cD5/AXrkNY=</latexit>∆t = T <latexit sha1_base64="+8FUkWl 9JVjn0Yhmp09+PMq7Ym0=">AB9XicbVA9SwNBEJ3zM8avqKXNYhCswl0 IaCMEtbCMkJhAcoS9zV6yZG/v3J0LhJDfYWOhILb+Fzv/jZvkCk18MPB4b 4aZeUEihUHX/XbW1jc2t7ZzO/ndvf2Dw8LR8aOJU814g8Uy1q2AGi6F4g0 UKHkr0ZxGgeTNYHg785sjro2IVR3HCfcj2lciFIyilfzOHZdICZJrUq53C 0W35M5BVomXkSJkqHULX51ezNKIK2SGtP23AT9CdUomOTfCc1PKFsSPu 8bamiETf+ZH70lJxbpUfCWNtSObq74kJjYwZR4HtjCgOzLI3E/z2imGV /5EqCRFrthiUZhKgjGZJUB6QnOGcmwJZVrYWwkbUE0Z2pzyNgRv+eV0iy XvErJ8x4qxepNlkcOTuEMLsCDS6jCPdSgAQye4Ble4c0ZOS/Ou/OxaF1zs pkT+APn8wd6aZES</latexit>∆t = 2T <latexit sha1_b ase64="O0RPvHRw/IJZ09PwLbtl4k 96bM0=">AB9XicbVA9SwNBEN2LX zF+RS1tFoNgFe40oI0Q1MIyQmICyR H2NnPJkr29c3cuEJ+h42Fgtj6X+z 8N26SKzT6YODx3gwz84JECoOu+Xk VlbX1jfym4Wt7Z3dveL+wYOJU82hw WMZ61bADEihoIECJbQSDSwKJDSD4c 3Mb45AGxGrOo4T8CPWVyIUnKGV/M4 tSGQU6RU9r3eLJbfszkH/Ei8jJZKh 1i1+dnoxTyNQyCUzpu25CfoTplFwC dNCJzWQMD5kfWhbqlgExp/Mj57SE6 v0aBhrWwrpXP05MWGRMeMosJ0Rw4F Z9mbif147xfDSnwiVpAiKLxaFqaQY 01kCtCc0cJRjSxjXwt5K+YBpxtHmV LAheMsv/yXNs7JXKXvefaVUvc7yJ MjckxOiUcuSJXckRpE4eyRN5Ia/ OyHl23pz3RWvOyWYOyS84H975ET </latexit>∆t = 3T <latexit sha1_base64="Ztha2fo3iGVJ75b/X8HaS3m094=">AB8X icbVBNSwMxFHzrZ61fVY9egkX0VDZS0GPRi8cK1lbapWSz2TY0yS5JVihLf4UXDwri1X/jzX9j2u5BWwcCw8w8t6EqeDG+v63t7K6tr6xWdoqb+/s7u 1XDg4fTJpylo0EYnuhMQwRVrW4F6SaERkK1g5HN1O/cS04Ym6t+OUBZIMFI85JdZJjz3hohFBZ/1K1a/5M6BlgtShQLNfuWrFyU0k0xZKogxXe ZFdEg0odZ1VHYl4MWTl0n7obrNYzv6tXGdFHCY7hBM4BwyU04Ba0AIKEp7hFd487b14797HPLriFTNH8Afe5w+QkZAR</latexit>ynNsiJtpwKNin3MsNSQkdkwLqOKiKZCfLZwhN06pQIxYl2T1k0U39P5EQaM5ahS0pih2bRm4r/ed3MxldBzlWaWabo/KM4E8gmaHo9irhm1IqxI4Rq7n λ0 <latexit sha1_base64="Ztha2fo3iGVJ75b/X8HaS3m094=">AB8X icbVBNSwMxFHzrZ61fVY9egkX0VDZS0GPRi8cK1lbapWSz2TY0yS5JVihLf4UXDwri1X/jzX9j2u5BWwcCw8w8t6EqeDG+v63t7K6tr6xWdoqb+/s7u 1XDg4fTJpylo0EYnuhMQwRVrW4F6SaERkK1g5HN1O/cS04Ym6t+OUBZIMFI85JdZJjz3hohFBZ/1K1a/5M6BlgtShQLNfuWrFyU0k0xZKogxXe ZFdEg0odZ1VHYl4MWTl0n7obrNYzv6tXGdFHCY7hBM4BwyU04Ba0AIKEp7hFd487b14797HPLriFTNH8Afe5w+QkZAR</latexit>ynNsiJtpwKNin3MsNSQkdkwLqOKiKZCfLZwhN06pQIxYl2T1k0U39P5EQaM5ahS0pih2bRm4r/ed3MxldBzlWaWabo/KM4E8gmaHo9irhm1IqxI4Rq7n λ0 <latexit sha1_base64="Ztha2fo3iGVJ75b/X8HaS3m094=">AB8X icbVBNSwMxFHzrZ61fVY9egkX0VDZS0GPRi8cK1lbapWSz2TY0yS5JVihLf4UXDwri1X/jzX9j2u5BWwcCw8w8t6EqeDG+v63t7K6tr6xWdoqb+/s7u 1XDg4fTJpylo0EYnuhMQwRVrW4F6SaERkK1g5HN1O/cS04Ym6t+OUBZIMFI85JdZJjz3hohFBZ/1K1a/5M6BlgtShQLNfuWrFyU0k0xZKogxXe ZFdEg0odZ1VHYl4MWTl0n7obrNYzv6tXGdFHCY7hBM4BwyU04Ba0AIKEp7hFd487b14797HPLriFTNH8Afe5w+QkZAR</latexit>ynNsiJtpwKNin3MsNSQkdkwLqOKiKZCfLZwhN06pQIxYl2T1k0U39P5EQaM5ahS0pih2bRm4r/ed3MxldBzlWaWabo/KM4E8gmaHo9irhm1IqxI4Rq7n λ0 EFEITO DOPPLER: LEMBRANDO DO QUE OCORRIA QUANTO A FONTE SE MOVIMENTAVA Quando discutimos o efeito Doppler devido ao movimento das fontes observamos que a mudança de frequência se dava porque a fonte estava mudando de lugar e gerando cada nova frente de onda num ponto diferente no espaço. Assim as frentes de ondas acabavam todas excêntricas. FONTE EM MOVIMENTO SUPERSÔNICO E OBSERVADOR EM REPOUSO <latexit sha1_base64="OoHnUMTfKHKutCSpgX5+x yUTug=">ACHicbVDLSsNAFJ34rPUVdSnIYBFclUQKuiwK4rKCtYUmhMlk0g6dTMLMpBhCdm78FTcuFMS tn+DOv3GaZqGtBy4czrl35t7jJ4xKZVnfxtLyuraem2jvrm1vbNr7u3fyzgVmHRxzGLR95EkjHLSVQx0k8 EQZHPSM8fX0393oQISWN+p7KEuBEachpSjJSWPIKd/IBQkKOPFyJ/Ljh9xRlGfwuig8s2E1rRJwkdgVaYA KHc/8coIYpxHhCjMk5cC2EuXmSCiKGSnqTipJgvAYDclAU4iIt283KGAJ1oJYBgLXVzBUv09kaNIyizydWe E1EjOe1PxP2+QqvDCzSlPUkU4n0UpgyqGE5DgQEVBCuWaYKwoHpXiEdIKx0dHUdgj1/8iLpnTXtVtO2b1u N9mWVRw0cgmNwCmxwDtrgBnRAF2DwCJ7BK3gznowX4934mLUuGdXMAfgD4/MHoUGaOw=</latexit>vF O movimento supersônico é o caso extremo deste fenômeno. A fonte tem velocidade maior que a velocidade de fase no gás e de fato vence a frente de onda que ela própria gerou. <latexit sha1_base64="ZHNFm7aul4+awZu3cbU6m 4LJoVo=">ACnicbVDLSsNAFJ3UV62vqEs3g0VwVRIRdFl047KCtYWmhMl02g6dR5iZFEPI1o2/4saFgrj 1C9z5N07TLT1wIXDOfO3HuimFtPO/bqaysrq1vVDdrW9s7u3vu/sG9lonCpI0lk6obIU0YFaRtqGkGyu CeMRIJ5pcz/zOlChNpbgzaUz6HI0EHVKMjJVCFwbFG5kigxOwyzgkXzIAkNFCrXkeR6da/hFYDLxC9JHZR ohe5XMJA4UQYzJDWPd+LT9DylDMSF4LEk1ihCdoRHqWCsSJ7mfFjk8scoADqWyJQws1N8TGeJapzynRy ZsV70ZuJ/Xi8xw8t+RkWcGCLw/KNhwqCRcBYLHFBFsGpJQgraneFeIwUwsaGV7Mh+IsnL5POWcM/b/j+7Xm 9eVXmUQVH4BicAh9cgCa4AS3QBhg8gmfwCt6cJ+fFeXc+5q0Vp5w5BH/gfP4Al8ebWA=</latexit>vsom <latexit sha1_base64="OoHnUMTfKHKutCSpgX5+x yUTug=">ACHicbVDLSsNAFJ34rPUVdSnIYBFclUQKuiwK4rKCtYUmhMlk0g6dTMLMpBhCdm78FTcuFMS tn+DOv3GaZqGtBy4czrl35t7jJ4xKZVnfxtLyuraem2jvrm1vbNr7u3fyzgVmHRxzGLR95EkjHLSVQx0k8 EQZHPSM8fX0393oQISWN+p7KEuBEachpSjJSWPIKd/IBQkKOPFyJ/Ljh9xRlGfwuig8s2E1rRJwkdgVaYA KHc/8coIYpxHhCjMk5cC2EuXmSCiKGSnqTipJgvAYDclAU4iIt283KGAJ1oJYBgLXVzBUv09kaNIyizydWe E1EjOe1PxP2+QqvDCzSlPUkU4n0UpgyqGE5DgQEVBCuWaYKwoHpXiEdIKx0dHUdgj1/8iLpnTXtVtO2b1u N9mWVRw0cgmNwCmxwDtrgBnRAF2DwCJ7BK3gznowX4934mLUuGdXMAfgD4/MHoUGaOw=</latexit>vF FONTE EM MOVIMENTO SUPERSÔNICO E OBSERVADOR EM REPOUSO A fonte ganha da frente de onda! <latexit sha1_base64="ZHNFm7aul4+awZu3cbU6m 4LJoVo=">ACnicbVDLSsNAFJ3UV62vqEs3g0VwVRIRdFl047KCtYWmhMl02g6dR5iZFEPI1o2/4saFgrj 1C9z5N07TLT1wIXDOfO3HuimFtPO/bqaysrq1vVDdrW9s7u3vu/sG9lonCpI0lk6obIU0YFaRtqGkGyu CeMRIJ5pcz/zOlChNpbgzaUz6HI0EHVKMjJVCFwbFG5kigxOwyzgkXzIAkNFCrXkeR6da/hFYDLxC9JHZR ohe5XMJA4UQYzJDWPd+LT9DylDMSF4LEk1ihCdoRHqWCsSJ7mfFjk8scoADqWyJQws1N8TGeJapzynRy ZsV70ZuJ/Xi8xw8t+RkWcGCLw/KNhwqCRcBYLHFBFsGpJQgraneFeIwUwsaGV7Mh+IsnL5POWcM/b/j+7Xm 9eVXmUQVH4BicAh9cgCa4AS3QBhg8gmfwCt6cJ+fFeXc+5q0Vp5w5BH/gfP4Al8ebWA=</latexit>vsom <latexit sha1_base64="ZHNFm7aul4+awZu3cbU6m 4LJoVo=">ACnicbVDLSsNAFJ3UV62vqEs3g0VwVRIRdFl047KCtYWmhMl02g6dR5iZFEPI1o2/4saFgrj 1C9z5N07TLT1wIXDOfO3HuimFtPO/bqaysrq1vVDdrW9s7u3vu/sG9lonCpI0lk6obIU0YFaRtqGkGyu CeMRIJ5pcz/zOlChNpbgzaUz6HI0EHVKMjJVCFwbFG5kigxOwyzgkXzIAkNFCrXkeR6da/hFYDLxC9JHZR ohe5XMJA4UQYzJDWPd+LT9DylDMSF4LEk1ihCdoRHqWCsSJ7mfFjk8scoADqWyJQws1N8TGeJapzynRy ZsV70ZuJ/Xi8xw8t+RkWcGCLw/KNhwqCRcBYLHFBFsGpJQgraneFeIwUwsaGV7Mh+IsnL5POWcM/b/j+7Xm 9eVXmUQVH4BicAh9cgCa4AS3QBhg8gmfwCt6cJ+fFeXc+5q0Vp5w5BH/gfP4Al8ebWA=</latexit>vsom <latexit sha1_base64="OoHnUMTfKHKutCSpgX5+xyUTug=">ACHicbVDLSsNAFJ34rPUVdSnIYBFcl UQKuiwK4rKCtYUmhMlk0g6dTMLMpBhCdm78FTcuFMStn+DOv3GaZqGtBy4czrl35t7jJ4xKZVnfxtLyuraem2jvrm1vbNr7u3fyzgVmHRxzGLR95EkjHLSVQx0k8EQZHPSM8fX0393oQISWN+p7KEuBEachpSjJSWPIK d/IBQkKOPFyJ/Ljh9xRlGfwuig8s2E1rRJwkdgVaYAKHc/8coIYpxHhCjMk5cC2EuXmSCiKGSnqTipJgvAYDclAU4iIt283KGAJ1oJYBgLXVzBUv09kaNIyizydWeE1EjOe1PxP2+QqvDCzSlPUkU4n0UpgyqGE5DgQEVB CuWaYKwoHpXiEdIKx0dHUdgj1/8iLpnTXtVtO2b1uN9mWVRw0cgmNwCmxwDtrgBnRAF2DwCJ7BK3gznowX4934mLUuGdXMAfgD4/MHoUGaOw=</latexit>vF <latexit sha1_base64="WtjzinxrlU4kzVpXGQRBeUYiwDI=">AB9HicbVBNS8NAEJ3Ur1q/qh69LBbBU0lE0ItQ1IPHCtYWmlA2027dLMJuxOh hP4NLx4UxKs/xpv/xm2bg7Y+GHi8N8PMvDCVwqDrfjuldW19Y3yZmVre2d3r7p/8GiSTDPeYolMdCekhkuheAsFSt5JNadxKHk7HN1M/fYT10Yk6gHKQ9iOlAiEoyilXz/lkukBMkVcXvVmlt3ZyDLxCtIDQo0e9Uv5+wLOYKmaTGdD03xSCnGgWTfFLxM8NTykZ0wLuWKhpzE+SzmyfkxCp9EiXalkIyU39P 5DQ2ZhyHtjOmODSL3lT8z+tmGF0GuVBphlyx+aIokwQTMg2A9IXmDOXYEsq0sLcSNqSaMrQxVWwI3uLy6R9VvfO653f15rXBd5lOEIjuEUPLiABtxBE1rAIVneIU3J3NenHfnY95acoqZQ/gD5/MHzyiQsg=</latexit>∆t = 0 <latexit sha1_base64="VHzpmnisfK3i/tDtRu5z2TD20Q=">AB9H icbVBNS8NAEJ3Ur1q/qh69LBbBU0mkoBehqAePFVpbaELZbDft0s0m7E6EUvo3vHhQEK/+G/+G7dtDtr6YODx3gwz8JUCoOu+0U1tY3NreK26Wd3b 39g/Lh0aNJMs14iyUy0Z2QGi6F4i0UKHkn1ZzGoeTtcHQ789tPXBuRqCaOUx7EdKBEJBhFK/n+HZdICZJr0uyVK27VnYOsEi8nFcjR6JW/H7CspgrZJ Ia0/XcFIMJ1SiY5NOSnxmeUjaiA961VNGYm2Ayv3lKzqzSJ1GibSkc/X3xITGxozj0HbGFIdm2ZuJ/3ndDKOrYCJUmiFXbLEoyiTBhMwCIH2hOUM5to 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<latexit sha1_base64="SjkEQJa5K9d98WNc6yQKXBRGtI=">AB/nicbVDLSsNAFJ3UV62 v+Ni5GSyCq5JIQZdFQVxWaG2hDWEynbRDJzNhZlKMIfgrblwoiFu/w51/47TNQlsPXDicy/3hPEjCrtON9WaWV1bX2jvFnZ2t7Z3bP3D+6VSCQmbSyYkN0AKcIoJ21NSPdWBIUBYx0gvH1O9M iFRU8JZOY+JFaMhpSDHSRvLto4mf9aNAPGR9TXkKb/Ictny76tScGeAycQtSBQWav3VHwicRIRrzJBSPdeJtZchqSlmJK/0E0VihMdoSHqGchQR5Wz63N4apQBDIU0xTWcqb8nMhQplUaB6YyQH qlFbyr+5/USHV56GeVxognH80VhwqAWcBoFHFBJsGapIQhLam6FeIQkwtoEVjEhuIsvL5POec2t1z3rl5tXBV5lMExOAFnwAUXoAFuQRO0AQaP4Bm8gjfryXqx3q2PeWvJKmYOwR9Ynz8s9pV9</ latexit>vFT O ângulo de Mach é dado por O número de Mach é definido como a razão <latexit sha1_base64="tn9WRz/X0O3rp/T53OPso/Rp4M=">ACK3icbZDLSsNAFIYn9V5vVZduBovgqiRS0I3g BcRlBWuFJoTJdGIH5xJmTsQS+jxufBU3LhTFre/hpO1Cqz8M/HznHM6cP8kEt+D715lZnZufmFxqbq8srq2XtvYvLY6N5S1qRba3CTEMsEVawMHwW4yw4hMBOskd2dlvXPjOVaXcEgY5Ekt4qnBJwK6dhJYrHEKfAYklPsJhagt7uMilIl+ 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Dentro do cone ele ouve uma mistura de sons. 1) Som com frequência emitido anteriormente e cujas frentes de onda o atingem (pela esquerda na figura) em ordem inversa que foram emitidas. 2) Som com frequência emitido posteriormente pela fonte e cujas frentes de onda o atingem (pela direita na figura) na ordem correta que foram emitidas <latexit sha1_base64="DxiwrYL9sraCKqtuFcum19JR+o=">ACTnicbZHNSxtBGMZn41eM1UZ79PJikOrBsCtCvQhiofSYQmOEbAizk9lkcD6WmXfF GvYJaFEzyshbnjmeUXdMh73qpqeKuV0zTKGHfkwGkxvqjEab0/4mCKufGKvGdiuLILXoT+J7XzTE97RVCZzlyzWaL0lwCGphECwNhOUM59oIyK/xdgY2oTxT9B9R8CNHik9+KznEzOmlG0Y+TxvnFPI8q2SV75IBE5As5J9Ji7QJI/fkD3kif4OH4DF4Dl5mrZVgPvOJvKpK9R+3DLSl</latexit>sO4/6EXorf9FLx4siJ18HGr0hYGH3/O+vDPJkUDsPwd1BZWl5ZXau1zY+bG59rG/vXDqTW8bzEhjrxLquBSat1Gg5FeZ5VQlkneS68Tv3PDrRNG/8RxnuKDrVIBaPoUb8+SD+fQqx5CkeQJxaygq46RexSsxtEaPQY3BGlSUAlMXd+9bRIv7m4R2UEFsxHOFhv94Im+G04K2I5qJB5tXq13/FA8NyxTUySZ3rRmG f 0 = f ✓ vsom |vsom − vF| ◆ <latexit sha1_base64="vHRADjV6+NPGVsgsU3mr63dDmQ=">ACTHicdZBLaxsxFIU1Tuqk7stNltlcYkpdCmamBNJNwaQskyhjg0eYzSyxhbW Y5DumJph/l83WTXP5FNFgmEQOXHorXTA4LDOfci6UsyKRyG4e+gsrP7rLq3/7z24uWr12/qbw+unMkt4x1mpLG9hDouheYdFCh5L7OcqkTybjL9ui7M26dMPo7zjM+UHSsRSoYR8N60n6/gukEueYhPi1FJWwGxYxCoxP4oYhZ6DM6osAaD8T/NxMz5fjJcQWzGe4IdhvRG2wqVg20Rr0yBrXQ7r1/HIsFx t>jUxS5/pRmOGgoBYFk7ysxbnjGWVTOuZ9bzV3A2KJYsS3vlkBKmx/miEZfr3RkGVc3OV+ElFceI2u0X4VNfPMf08KITOcuSarS5KcwloYAEWRsJyhnLuDWVW+LcCm1DPEz3+mocQbX523Q/taKTVhR9O2m0z9Y89skROSZNEpFT0iYX5J0CM/yQ25I/fBr+A2eAgeV6OVYL1zSP5RpfoHn7Kzlw=</latexi f 0 = f ✓ vsom vsom + vF ◆ <latexit sha1_base64="OoHnUMTfKHKutCSpgX5+x yUTug=">ACHicbVDLSsNAFJ34rPUVdSnIYBFclUQKuiwK4rKCtYUmhMlk0g6dTMLMpBhCdm78FTcuFMS tn+DOv3GaZqGtBy4czrl35t7jJ4xKZVnfxtLyuraem2jvrm1vbNr7u3fyzgVmHRxzGLR95EkjHLSVQx0k8 EQZHPSM8fX0393oQISWN+p7KEuBEachpSjJSWPIKd/IBQkKOPFyJ/Ljh9xRlGfwuig8s2E1rRJwkdgVaYA KHc/8coIYpxHhCjMk5cC2EuXmSCiKGSnqTipJgvAYDclAU4iIt283KGAJ1oJYBgLXVzBUv09kaNIyizydWe E1EjOe1PxP2+QqvDCzSlPUkU4n0UpgyqGE5DgQEVBCuWaYKwoHpXiEdIKx0dHUdgj1/8iLpnTXtVtO2b1u N9mWVRw0cgmNwCmxwDtrgBnRAF2DwCJ7BK3gznowX4934mLUuGdXMAfgD4/MHoUGaOw=</latexit>vF FONTE EM MOVIMENTO SUPERSÔNICO E OBSERVADOR EM REPOUSO Quebra da barreira do som Não existe um cone de Mach mas um plano. Quando a fonte passa pelo observador ele ouve um ruído alto (estouro) devido a superposição de todas as frentes de ondas que se propagam (na figura) para direita. Depois ele percebe o som emitido pela fonte (que se afasta) e que chega nele se propagando para a esquerda (na figura) e cuja frequência é a metade da frequência realmente emitida pela fonte. Efeito Doppler da Luz Não há meio de propagação. As ondas eletromagnéticas se propagam no vácuo. Importa somente a velocidade relativa entre fonte e observador <latexit sha1_base64="94pNZEITFn/lWrV3hLk/Fnd0PY=">ACE 3icbZDNSgMxFIUz9a/Wv1GXboJFVMQ6kYKCEU3LitYW+iUkzbWgmMyaZQhn6DG58FTcuFMStG3e+jZl2Ftp6IPBx7r3c3ONFnCntON9Wbm5+Y XEpv1xYWV1b37A3t+5VGEtCayTkoWx4WFHOBK1pjltRJLiwO07vWv03p9QKViobjTw4i2AtwVzGcEa2O17UN/xL60L2ArnqQ2vUlJglE8AgOT gcpXg8wbZdErOWHAWUAZFkKnatr/cTkjigApNOFaqiZxItxIsNSOcjgpurGiESR93adOgwAFVrWR80gjuGacD/VCaJzQcu78nEhwoNQw80xlg3 VPTtdT8r9aMtX/eSpiIYk0FmSzyYw51CN8YIdJSjQfGsBEMvNXSHrYpKJNigUTApo+eRbqpyVULiF0Wy5WrI8mAH7IDgMAZqIAbUAU1QMAje Aav4M16sl6sd+tj0pqzsplt8EfW5w8Q5p9</latexit> f 0 = f s 1 + v/c 1 − v/c A expressão Doppler Relativística para a frequência observada é onde “v" é a velocidade relativa entre fonte e observador e seu sinal indica se estão se aproximando (+) ou se afastando (-) e “c" é a velocidade da luz. <latexit sha1_base64="bBl4i2oJ8KP1Oode6I/v2G4pSv4=">ACBX icbVDLSgMxFM3UV62vUZfdBIvgqs6USluKUHTjsoK1hc5QMmDU0yQ5IRytCFG3/FjQsFces/uPNvTB8LbT1wL4dz7iW5J4gZVdpxvq3M2vrG5lZ2O7 ezu7d/YB8e3asokZi0cMQi2QmQIowK0tJUM9KJUE8YKQdjK6nfvuBSEUjcafHMfE5GgaUoy0kXp2HsNLWKrVoFev1EpeHZYvqZzeA5Vzy4RWcGuE rcBSmABZo9+8vrRzjhRGjMkFJd14m1nyKpKWZkvMSRWKER2hAuoYKxIny09kRE3hqlD4MI2lKaDhTf2+kiCs15oGZ5EgP1bI3Ff/zuokOq35KRZxoIv D8oTBhUEdwmgjsU0mwZmNDEJbU/BXiIZIa5NbzoTgLp+8Stqlolsu5tudC4WuSRBXlwAs6ACyqgAW5AE7QABo/gGbyCN+vJerHerY/5aMZa7ByDP7 A+fwDIhZQt</latexit>c = 299 792 458 m/s Efeito Doppler da Luz Desvio para o vermelho ( REDSHIFT ) Uma fonte de luz vai parecer mais avermelhada* quando for for vista se afastando do observador <latexit sha1_base64="7WoEwgk+3mN0flfHUZtQdxHTihU=">AB73icbVBN S8NAEJ34WetX1aOXxSJ6KokU9OCh6MVjBWsKbSib7aRdutmE3Y1Qn+EFw8K4tW/481/47bNQVsfDzem2FmXpgKro3rfjsrq2vrG5ulrfL2zu7efuXg8FEnmWLYol IVDukGgWX2DLcCGynCmkcCvTD0e3U959QaZ7IBzNOMYjpQPKIM2qs5Edn5JpEpFepujV3BrJMvIJUoUCzV/nq9hOWxSgNE1TrjuemJsipMpwJnJS7mcaUshEdYMdSW TiGEzgHDy6hAXfQhBYwGMEzvMKbkzovzrvzMW9dcYqZI/gD5/MHBvaOiA=</latexit>PUQT47d0JOrdInUaJsSUNm6u+JnMZaj+PQdsbUDPWiNxX/8zqZia6CnMs0MyjZfFGUCWISMv2d9LlCZsTYEsoUt7cSNqSKMmMTKtsQvMWXl4l/UfPqNc+7r1cbN0UeJ f 0 < f * O efeito Doppler relativístico vale para todo o espectro de ondas-eletromagnéticas não só para a porção visível ao olho humano. Assim “avermelhar" e “azular" neste contexto devem ser considerados metaforicamente no sentido de abaixar ou aumentar a frequência. Efeito Doppler da Luz Desvio para o azul ( BLUESHIFT ) Uma fonte de luz vai parecer mais azulada* quando for for vista se aproximando do observador * O efeito Doppler relativístico vale para todo o espectro de ondas-eletromagnéticas não só para a porção visível ao olho humano. Assim “avermelhar" e “azular" neste contexto devem ser considerados metaforicamente no sentido de abaixar ou aumentar a frequência. <latexit sha1_base64="vS0HrCHaQFArtjWxTQu3ErfbnE=">AB73 icbVBNS8NAEJ34WetX1aOXxSJ6KokU9CRFLx4rWFNoQ9lsJ+3SzSbsboQS+iO8eFAQr/4db/4bt20O2vpg4PHeDPzwlRwbVz321lZXVvf2Cxtlbd3dv f2KweHjzrJFMWS0Si2iHVKLjEluFGYDtVSONQoB+Obqe+/4RK80Q+mHGKQUwHkecUWMlPzoj1yQivUrVrbkzkGXiFaQKBZq9yle3n7AsRmYoFp3PD WwIVWUGZtQ2YbgLb68TPyLmleved59vdq4KfIowTGcwDl4cAkNuIMmtIDBCJ7hFd6c1Hlx3p2PeuKU8wcwR84nz8KBo6K</latexit>c1QU6V4UzgpNzNKaUjegAO5ZKGqMO8tm5E3JqlT6JEmVLGjJTf0/kNZ6HIe2M6ZmqBe9qfif18lMdBXkXKaZQcnmi6JMEJOQ6e+kzxUyI8aWUKa4vZ f 0 > f Efeito Doppler da Luz Aproximação para velocidades relativas pequenas em relação à velocidade da Luz <latexit sha1_base64="94pNZEI TFn/lWrV3hLk/Fnd0PY=">ACE3icbZDNSgMxFIUz9a/Wv1GXboJFV MQ6kYKCEU3LitYW+iUkzbWgmMyaZQhn6DG58FTcuFMStG3e+jZl2F tp6IPBx7r3c3ONFnCntON9Wbm5+YXEpv1xYWV1b37A3t+5VGEtCayTko Wx4WFHOBK1pjltRJLiwO07vWv03p9QKViobjTw4i2AtwVzGcEa2O17 UN/xL60L2ArnqQ2vUlJglE8AgOTgcpXg8wbZdErOWHAWUAZFkKnat r/cTkjigApNOFaqiZxItxIsNSOcjgpurGiESR93adOgwAFVrWR80gjuG acD/VCaJzQcu78nEhwoNQw80xlg3VPTtdT8r9aMtX/eSpiIYk0FmSzyY w51CN8YIdJSjQfGsBEMvNXSHrYpKJNigUTApo+eRbqpyVULiF0Wy5Wr rI8mAH7IDgMAZqIAbUAU1QMAjeAav4M16sl6sd+tj0pqzsplt8EfW5 w8Q5p9</latexit> f 0 = f s 1 + v/c 1 − v/c Se então a expressão <latexit sha1_base64="/TzH7h QKdcBYC2rHqz9iEgNAjA=">AB8HicbVA9SwNBEJ2LXzF+nVraLAbBKt5 KQIsUQRvLCMYEkiPsbfaSJXt75+5eIBz5EzYWCmLrz7Hz37hJrtDEBwOP9 2aYmRckgmvjed9OYW19Y3OruF3a2d3bP3APjx51nCrKmjQWsWoHRDPBJWs abgRrJ4qRKBCsFYxuZ35rzJTmsXwk4T5ERlIHnJKjJXa4wuKajWEe27Zq 3hzoFWCc1KGHI2e+9XtxzSNmDRUEK072EuMnxFlOBVsWuqmiWEjsiAdSy VJGLaz+b3TtGZVfojJUtadBc/T2RkUjrSRTYzoiYoV72ZuJ/Xic14bWfc Zmkhkm6WBSmApkYzZ5Hfa4YNWJiCaGK21sRHRJFqLERlWwIePnlVdK6rOB qBeP7arl+k+dRhBM4hXPAcAV1uIMGNIGCgGd4hTfnyXlx3p2PRWvByWeO4 Q+czx/D3470</latexit>v/c << 1 usando que e para fica <latexit sha1_base64="smMCUqE keOrXP0Bb9ouHfSy3Dc=">ACBHicbVBNSwMxEM3Wr1q/Vr3pJVgEoVA 3paDHohePFawtdJeSTbNtaLK7TbLSshS8+Fe8eFAQr/4Ib/4b03YP2vpg4 PHeDPz/JgzpR3n28qtrK6tb+Q3C1vbO7t79v7BvYoSWiDRDySLR8ryl IG5pTluxpFj4nDb9wfXUbz5QqVgU3ulxTD2BeyELGMHaSB37yFVDqVNUG k2gq5igQ4hgCY7OK7BjF52yMwNcJigjRZCh3rG/3G5EkFDThWqo2cWHs plpoRTicFN1E0xmSAe7RtaIgFV46+2ECT43ShUEkTYUaztTfEykWSo2Fb zoF1n216E3F/7x2oNL2VhnGgakvmiIOFQR3AaCOwySYnmY0MwkczcCk fS0y0ia1gQkCLy+TZqWMqmWEbqvF2lWRx4cgxNwBhC4ADVwA+qgAQh4B M/gFbxZT9aL9W59zFtzVjZzCP7A+vwB3wyWKg=</latexit>p 1 + x ' 1 + x/2 <latexit sha1_base64="h1ucMgh4FxmHc8f+jEwjPVDq8=">AB7nicbVBNSwMxEJ2tX7V+VT16CRbBU9lIQ89FL14rGA/oF1KNs2sdlkSbJi Kf0PXjwoiFd/jzf/jWm7B219MPB4b4aZeWEiuLG+/+3l1tY3Nrfy24Wd3b39g+LhUdOoVFPWoEo3Q6JYJL1rDcCtZONCNxKFgrHN3M/NYj04YreW/HCQtiMpA84pRYJzWfULWKcK9Y8sv+HGiV4IyUIEO9V/zq9hVNYyYtFcSYDvYTG0yItpwKNi10U8MSQkdkwDqOShIzE0zm107RmVP6KFLalbRorv6emJDY mHEcus6Y2KFZ9mbif14ntdFVMOEyS2TdLEoSgWyCs1eR32uGbVi7AihmrtbER0STah1ARVcCHj5VXSuijShnju0qpdp3lkYcTOIVzwHAJNbiFOjSAwgM8wyu8ecp78d69j0VrzstmjuEPvM8fmzWOUA=</latexit>x << 1 <latexit sha1_base64="lINLq3k Yen0+1kNJv4aqDL5jRc=">AB/3icbVBNSwMxEM3Wr1q/VsWTl2ARK0L dSEGPRS8eK1hbaJeSTbNtaJdk2yhLAX/ihcPCuLVv+HNf2Pa7kFbHw83 pthZl4Qc6aN5307uaXldW1/HphY3Nre8fd3XvQUaIrZOIR6oZYE05k7R umOG0GSuKRcBpIxjcTPzGkCrNInlvRjH1Be5JFjKCjZU67kF40tZM0EcYw hJE8AwOz8lpxy16ZW8KuEhQRogQ63jfrW7EUkElYZwrHULebHxU6wMI5y OC+1E0xiTAe7RlqUSC6r9dHr+GB5bpQvDSNmSBk7V3xMpFlqPRGA7BTZ9P e9NxP+8VmLCKz9lMk4MlWS2KEw4NBGcZAG7TFi+MgSTBSzt0LSxwoTYxM +S8O/Ox6w152Qz+APnM8fJDuTeQ=</latexit>r2BDQ/MuLpHFRpUyQneVYvU6yMPDsERKAELkEV3IaqAMCUvAMXsGb8 f 0 ' f(1 + v/c) O que é semelhante ao caso do Doppler no som para o caso que as velocidades de fonte e de observador são muito menores que a velocidade do som. 1 p1 − x ' 1 + x/2