{"id":11676,"date":"2024-11-28T15:17:40","date_gmt":"2024-11-28T15:17:40","guid":{"rendered":"https:\/\/fisicaevestibular.com.br\/novo\/?page_id=11676"},"modified":"2024-12-03T14:15:19","modified_gmt":"2024-12-03T14:15:19","slug":"efeito-doppler-en","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/ondulatoria\/acustica\/efeito-doppler-en\/","title":{"rendered":"Doppler Effect – EN"},"content":{"rendered":"

Doppler effect<\/span><\/b><\/p>\n

It refers to the\u00a0<\/span><\/b>variation in frequency noticed\u00a0<\/span><\/b>by an\u00a0<\/span><\/b>observer\u00a0<\/span><\/b>when the\u00a0<\/span><\/b>distance between him and a wave source is increasing or decreasing.<\/span><\/b><\/p>\n

When\u00a0<\/span><\/b>the source and observer come closer together,\u00a0<\/span><\/b>the\u00a0<\/span><\/b>latter will perceive the sound emitted by the source as higher pitched\u00a0<\/span><\/b>(higher frequency, receives a greater number of wave fronts in the unit of time) than\u00a0<\/span><\/b>it would perceive if the source and observer were stationary.<\/span><\/b><\/p>\n

In this case, the\u00a0<\/span><\/b>apparent wavelength perceived by the observer will be smaller\u00a0<\/span><\/b>than the\u00a0<\/span><\/b>wavelength emitted by the source (observer O\u00a0<\/span><\/b>1<\/span><\/b><\/sub>\u00a0\u00a0in the figures below).<\/span><\/b><\/p>\n

\"\"<\/p>\n

When\u00a0<\/span><\/b>the source and observer are far apart,\u00a0<\/span><\/b>the\u00a0<\/span><\/b>latter will perceive the sound emitted by the source as lower\u00a0<\/span><\/b>(lower frequency, receives fewer wave fronts in the unit of time) than\u00a0<\/span><\/b>they would if the source and observer were stationary.<\/span><\/b><\/p>\n

In this case, the\u00a0<\/span><\/b>apparent wavelength perceived by the observer will be greater than the wavelength emitted by the source (observer O2\u00a0<\/span><\/b>in<\/span><\/b><\/sub>\u00a0\u00a0the figures above).<\/span><\/b><\/p>\n

Note that the\u00a0<\/span><\/b>ambulance driver does not notice any change in the sound emitted by the siren as they move together.<\/span><\/b><\/p>\n

If\u00a0<\/span><\/b>we call V the speed of sound,\u00a0<\/span><\/b>V\u00a0<\/b>f<\/b><\/sub>\u00a0\u00a0the speed of the source, V\u00a0<\/b>o<\/b><\/sub>\u00a0\u00a0the speed of the observer, f the real frequency emitted by the source\u00a0<\/b>, the\u00a0<\/b>apparent frequency f\u00a0<\/b>a<\/b><\/sub>\u00a0\u00a0perceived by the observer\u00a0<\/b>will be\u00a0<\/b>given\u00a0<\/b>by\u00a0<\/b>the expression:<\/b><\/span>\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

\"\"<\/p>\n

Rule of signs<\/span><\/b><\/p>\n

\"\"<\/p>\n

By directing the observer’s trajectory towards the source\u00a0<\/span><\/b>, the\u00a0<\/span><\/b>signs\u00a0<\/span><\/b>of\u00a0<\/span><\/b>V\u00a0<\/span><\/b>o<\/span><\/b><\/sub>\u00a0and V\u00a0<\/span><\/b>f<\/span><\/b><\/sub>\u00a0will be positive in favor of this<\/span><\/b><\/p>\n

guidance and negatives against that guidance.<\/span><\/b><\/p>\n

Carefully analyze\u00a0<\/span><\/b>the examples of the\u00a0<\/span><\/b>signal rules\u00a0<\/span><\/b>given below:<\/span><\/b><\/p>\n

\"\"<\/p>\n

If observer or source is at rest:<\/span><\/b><\/p>\n

\"\"<\/p>\n

Doppler effect for movements in any direction<\/span><\/b><\/p>\n

In the above studies\u00a0<\/span><\/b>we assumed\u00a0<\/span><\/b>that the\u00a0<\/span><\/b>source and the observer were in the same direction of motion.<\/span><\/b><\/p>\n

But the\u00a0<\/span><\/b>source\u00a0<\/span><\/b>can\u00a0<\/span><\/b>move in a direction that forms an angle \u03b8 with the direction connecting the source to the observer,\u00a0<\/span><\/b>as in the figure.<\/span><\/b>\"\"<\/p>\n

Only the\u00a0<\/span><\/b>component of velocity in the direction of the observer contributes to the Doppler effect.<\/span><\/b><\/p>\n

\"\"<\/p>\n

What you should know, information and tips<\/span><\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Rule of signs<\/span><\/b><\/p>\n

\"\"<\/p>\n

By directing the observer’s trajectory towards the source\u00a0<\/span><\/b>, the\u00a0<\/span><\/b>signs\u00a0<\/span><\/b>of\u00a0<\/span><\/b>V\u00a0<\/span><\/b>o<\/span><\/b><\/sub>\u00a0and V\u00a0<\/span><\/b>f<\/span><\/b><\/sub>\u00a0will be positive in favor of this<\/span><\/b><\/p>\n

guidance and negatives against that guidance.<\/span><\/b><\/p>\n

\"\"<\/p>\n

Doppler effect for movements in any direction<\/span><\/b><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Beat frequency \u2013 Sound interferenceSound interference<\/span><\/b><\/p>\n

 <\/p>\n

<\/b>Beat frequency\u00a0<\/span><\/b>occurs\u00a0<\/b><\/span>when\u00a0<\/span><\/b>two or more sound waves overlap at the same point.<\/span><\/b><\/p>\n

Let us suppose\u00a0<\/span><\/b>two sound waves of slightly different frequencies\u00a0<\/span><\/b>, one of\u00a0<\/span><\/b>f\u00a0<\/span><\/b>A =<\/span><\/b><\/sub>\u00a0100Hz\u00a0<\/span><\/b>and the other of\u00a0<\/span><\/b>f\u00a0<\/span><\/b>B<\/span><\/b><\/sub>\u00a0= 110Hz.<\/span><\/b><\/p>\n

Then\u00a0<\/span><\/b>you will hear\u00a0<\/span><\/b>a\u00a0<\/span><\/b>loud sound\u00a0<\/span><\/b>(constructive interference) and\u00a0<\/span><\/b>then\u00a0<\/span><\/b>a\u00a0<\/span><\/b>soft sound\u00a0<\/span><\/b>(destructive interference) and so\u00a0<\/span><\/b>on.\u00a0<\/span><\/b>This\u00a0<\/span><\/b>phenomenon is called debating\u00a0\u00a0<\/span><\/b>(figure).<\/span><\/b><\/p>\n

Note that the\u00a0<\/span><\/b>resulting wave presents points where the amplitude is maximum\u00a0<\/span><\/b>(loud sounds, constructive interference) as in points\u00a0<\/span><\/b>A, C and E\u00a0<\/span><\/b>, it decreases and\u00a0<\/span><\/b>practically disappears or is cancelled out (destructive interference)\u00a0<\/span><\/b>as in points\u00a0<\/span><\/b>B, D and F.<\/span><\/b>\"\"<\/p>\n

The\u00a0<\/span><\/b>beat frequency\u00a0<\/span><\/b>is defined as\u00a0<\/span><\/b>f\u00a0<\/span><\/b>beat<\/span><\/b><\/sub>\u00a0= f\u00a0<\/span><\/b>major<\/span><\/b><\/sub>\u00a0\u00a0\u2013 f\u00a0<\/span><\/b>minor<\/span><\/b><\/sub>\u00a0.<\/span><\/b><\/b><\/p>\n

The\u00a0<\/span><\/b>phenomenon of beating\u00a0<\/span><\/b>is often used in the\u00a0<\/span><\/b>tuning of musical instruments.\u00a0<\/span><\/b>If the frequencies of the tuning source and the instrument are different, a beating sound is heard. The\u00a0<\/span><\/b>frequency of the beating sound decreases as the instrument is tuned\u00a0<\/span><\/b>, and when\u00a0<\/span><\/b>it disappears, the instrument is in tune<\/span><\/b>\u00a0.<\/span><\/p>\n

Uses of the Doppler Effect<\/span><\/b><\/p>\n

\"\"\u00a0In medical diagnostics, ultrasound or sonography\u00a0<\/span><\/b>is a\u00a0<\/b>diagnostic method\u00a0<\/b>that uses the\u00a0<\/b>echo produced by sound to see in real time the shadows produced by the body’s structures and organs\u00a0<\/b>.<\/b><\/span>\u00a0\"\"\u00a0<\/b>\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

<\/b>Ultrasound devices\u00a0<\/span><\/b>generally\u00a0<\/b><\/span>use a\u00a0<\/span><\/b>frequency\u00a0<\/span><\/b>close to 1 MHz,\u00a0<\/span><\/b>emitted\u00a0<\/span><\/b>by a\u00a0<\/span><\/b>sound source placed in contact with the skin\u00a0<\/span><\/b>and\u00a0<\/span><\/b>receiving the generated echoes,\u00a0<\/span><\/b>which are\u00a0<\/span><\/b>interpreted\u00a0<\/span><\/b>through\u00a0<\/span><\/b>computer graphics.<\/span><\/b><\/b><\/p>\n

Depending on the\u00a0<\/span><\/b>density and composition of the body’s internal structures,\u00a0<\/span><\/b>the\u00a0<\/span><\/b>attenuation\u00a0<\/span><\/b>and\u00a0<\/span><\/b>phase shift of the emitted signals\u00a0<\/span><\/b>varies, making it\u00a0<\/span><\/b>possible to translate them into a gray scale, which will form the image of the internal organs.<\/span><\/b><\/p>\n

\"\"<\/p>\n

However, there is\u00a0<\/span><\/b>ultrasound equipment\u00a0<\/span><\/b>that,\u00a0<\/span><\/b>in addition to images,\u00a0<\/span><\/b>allows\u00a0<\/span><\/b>the\u00a0<\/b><\/span>evaluation\u00a0<\/span><\/b>of blood movement speeds.<\/b><\/span><\/b><\/b><\/p>\n

This equipment\u00a0<\/span><\/b>compares the frequency of the emitted ultrasound\u00a0<\/span><\/b>with the\u00a0<\/span><\/b>frequency of the reflected ultrasound and,\u00a0<\/span><\/b>through the\u00a0<\/span><\/b>Doppler Effect, determines the displacement speeds, knowledge of which is very important information for medical diagnoses in the following areas:<\/span><\/b><\/p>\n

\"\"\u00a0Study of\u00a0<\/span><\/b>arteries and veins;<\/span><\/b><\/p>\n

\"\"\u00a0Detection of\u00a0<\/span><\/b>venous or arterial thrombosis;<\/span><\/b><\/p>\n

\"\"\u00a0Arterial stenoses\u00a0<\/span><\/b>and\/or\u00a0<\/span><\/b>occlusions;<\/span><\/b><\/p>\n

\"\"\u00a0Aneurysms;<\/span><\/b><\/p>\n

\"\"\u00a0<\/b>Preoperative\u00a0<\/b>mapping of varicose veins;<\/b><\/span><\/b><\/p>\n

\"\"\u00a0Pregnancy\u00a0<\/span><\/b>for measuring\u00a0<\/span><\/b>maternal-fetal blood flow;<\/span><\/b><\/p>\n

\"\"\u00a0Diseases of the renal arteries\u00a0<\/span><\/b>(narrowings, obstructions and dilations).<\/span><\/b><\/p>\n

 <\/p>\n

\"\"\u00a0The\u00a0<\/span><\/b>operation of Doppler radar\u00a0<\/span><\/b>is based on the\u00a0<\/span><\/b>movements of the objects.\u00a0<\/span><\/b>The device\u00a0<\/span><\/b>emits\u00a0<\/span><\/b>an\u00a0<\/span><\/b>electromagnetic wave with a continuous and constant frequency (f’).<\/span><\/b><\/b><\/p>\n

If the\u00a0<\/span><\/b>moving body\u00a0<\/span><\/b>(e.g. automobile) in question is\u00a0<\/span><\/b>moving towards the source, the radar receiver will identify an increase in frequency (f”).<\/span><\/b><\/p>\n

\"\"<\/p>\n

The\u00a0<\/span><\/b>difference between the emitted (f’) and reflected (f”) frequencies\u00a0<\/span><\/b>will be\u00a0<\/span><\/b>translated by the decoder\u00a0<\/span><\/b>in the radar as a\u00a0<\/span><\/b>speed value.<\/span><\/b><\/b><\/p>\n

This\u00a0<\/span><\/b>type of radar\u00a0<\/span><\/b>also works when the\u00a0<\/span><\/b>vehicle is moving away.<\/span><\/b><\/p>\n

Again, what is at stake is the\u00a0<\/span><\/b>difference between the emission and reception frequencies\u00a0<\/span><\/b>, which allow us to evaluate the\u00a0<\/span><\/b>speed of the reflecting surface.<\/span><\/b><\/p>\n

<\/b>Air traffic control<\/span><\/b><\/a>\u00a0uses\u00a0\u00a0<\/b><\/span>\u00a0radar to track\u00a0\u00a0<\/span><\/b>planes<\/span><\/b><\/a>\u00a0\u00a0on the ground and in the air, and also to\u00a0<\/span><\/b>guide pilots to make smooth landings.<\/span><\/b><\/p>\n

<\/b>NASA uses them to map the Earth and other planets,\u00a0<\/span><\/b>to\u00a0<\/b><\/span>track\u00a0<\/span><\/b>satellites\u00a0\u00a0<\/span><\/b>and<\/span><\/b><\/a>\u00a0\u00a0space debris, and to help maneuver its aircraft.<\/span><\/b><\/p>\n

\"\"<\/p>\n

Meteorologists\u00a0<\/span><\/b>use radar to\u00a0<\/b>track storms,\u00a0\u00a0<\/b>hurricanes<\/b><\/a><\/span>\u00a0,\u00a0<\/span><\/b>\u00a0and\u00a0\u00a0<\/b>tornadoes<\/b><\/a>\u00a0.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

Even the\u00a0<\/span><\/b>device that makes store doors open automatically is a type of radar.<\/span><\/b><\/p>\n

\"\"\u00a0The\u00a0<\/span><\/b>Doppler effect\u00a0<\/span><\/b>is also\u00a0<\/span><\/b>valid for light\u00a0<\/span><\/b>(transverse electromagnetic wave).<\/span><\/b><\/p>\n

Thus, the\u00a0<\/span><\/b>frequency of light increases\u00a0<\/span><\/b>(the\u00a0<\/span><\/b>color of light\u00a0<\/span><\/b>tends towards\u00a0<\/span><\/b>blue\u00a0<\/span><\/b>) when the\u00a0<\/span><\/b>observer-source distance is decreasing\u00a0<\/span><\/b>and\u00a0<\/span><\/b>decreases\u00a0<\/span><\/b>(the\u00a0<\/span><\/b>color of light\u00a0<\/span><\/b>tends towards\u00a0<\/span><\/b>red\u00a0<\/span><\/b>) when the\u00a0<\/span><\/b>observer-source distance is increasing\u00a0<\/span><\/b>. The\u00a0<\/span><\/b>relative velocity between the observer and the source is very large.<\/span><\/b><\/p>\n

Thus, due to the\u00a0<\/span><\/b>Doppler effect, the colors of a star’s electromagnetic spectrum appear<\/span><\/b><\/p>\n

\"\"<\/p>\n

shifted to the red, if the observed star is moving away\u00a0<\/span><\/b>, or\u00a0<\/span><\/b>shifted to the blue, if the star is approaching us.<\/span><\/b><\/p>\n

In astronomy, the\u00a0<\/span><\/b>Doppler effect is used\u00a0<\/span><\/b>to measure the\u00a0<\/span><\/b>relative speed of stars\u00a0<\/span><\/b>and other luminous celestial bodies in\u00a0<\/span><\/b>relation to Earth.<\/span><\/b><\/p>\n

These measurements\u00a0<\/span><\/b>led scientists to conclude that the\u00a0<\/span><\/b>universe is expanding, as the color of these luminous celestial bodies shows a greater red shift, which indicates that the distance between them and us is increasing.<\/span><\/b><\/p>\n

\"\"\u00a0If you want, you can\u00a0<\/span><\/b>check the solutions\u00a0<\/span><\/b>of some exercises that\u00a0<\/span><\/b>may be useful\u00a0<\/span><\/b>and that I selected\u00a0<\/span>\"\"\u00a0<\/b>are\u00a0<\/span><\/b>the\u00a0<\/span><\/b>numbers, 04, 09, 11, 16, 17, 19 and 29.<\/span><\/b><\/p>\n

\"\"<\/p>\n

See the resolution of some interesting exercises:<\/span><\/b><\/p>\n

01-(FUVEST-SP)\u00a0<\/span><\/b>A\u00a0<\/span><\/b>sound wave\u00a0<\/span><\/b>considered flat,\u00a0<\/span><\/b>coming from a siren at rest,\u00a0<\/span><\/b>propagates in\u00a0<\/span><\/b>still air, in the horizontal direction,\u00a0<\/span><\/b>with\u00a0<\/span><\/b>a speed V equal to 330 m\/s and a wavelength equal to 16.5 cm.<\/span><\/b>\"\"<\/p>\n

In the\u00a0<\/span><\/b>region where the wave is propagating,\u00a0<\/span><\/b>an\u00a0<\/span><\/b>athlete runs,\u00a0<\/span><\/b>on a\u00a0<\/span><\/b>horizontal track,\u00a0<\/span><\/b>at\u00a0<\/span><\/b>a speed U equal to 6.60 m\/s,\u00a0<\/span><\/b>forming an\u00a0<\/span><\/b>angle of 60\u00b0 with the direction of propagation of the wave\u00a0<\/span><\/b>.<\/span><\/b><\/p>\n

Determine\u00a0<\/span><\/b>the\u00a0<\/span><\/b>approximate frequency\u00a0<\/span><\/b>of the\u00a0<\/span><\/b>sound heard by the athlete.<\/span><\/b><\/p>\n

Resolution:<\/span><\/b><\/p>\n

The\u00a0<\/span><\/b>wave propagation speed V and the observer (receiver) speed U\u00a0<\/span><\/b>must be in the\u00a0<\/span><\/b>same direction.<\/span><\/b><\/p>\n

Only the\u00a0<\/span><\/b>horizontal component (U\u00a0<\/span><\/b>x<\/span><\/b><\/sub>\u00a0) of the observer’s\u00a0\u00a0<\/b><\/span>velocity (U)\u00a0<\/span><\/b>influences the movement\u00a0<\/b>, since the wave fronts are flat,\u00a0<\/b>propagating horizontally and to the right. Note that the vertical component of U does not reach the observer\u00a0<\/b>and you\u00a0<\/b>must consider only the component on the line that connects the observer to the source:\u00a0<\/b>(see figures).<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

\"\"<\/p>\n

Projecting U in the direction of V\u00a0<\/span>\"\"<\/b>U\u00a0<\/b>x<\/b><\/sub>\u00a0= Ucos60\u00a0<\/b>o<\/b><\/sup>\u00a0\u00a0 U\u00a0<\/b>x<\/b><\/sub>\u00a0= 6.6.0.5\u00a0\u00a0<\/b>U\u00a0<\/b>x<\/b><\/sub>\u00a0= 3.3 m\/s.<\/b><\/span>\u00a0<\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b><\/b>\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b>\u00a0\u00a0<\/b><\/p>\n

Calculation of the\u00a0<\/span><\/b>source frequency\u00a0<\/span><\/b>using the\u00a0<\/span><\/b>fundamental wave equation\u00a0\u00a0<\/span>\"\"<\/b>\u00a0V = \u03bbf\u00a0\u00a0<\/span>\"\"\u00a0 330 = 0.165f\u00a0\u00a0<\/span>\"\"\u00a0\u00a0<\/b>f = 2,000Hz.<\/span><\/b><\/p>\n

The\u00a0<\/span><\/b>source speed is zero\u00a0<\/span><\/b>, since the\u00a0<\/span><\/b>siren\u00a0<\/span><\/b>is at\u00a0<\/span><\/b>rest\u00a0<\/span><\/b>V\u00a0<\/b>F<\/b><\/sub>\u00a0= 0<\/b><\/span>\u00a0\"\"<\/b><\/b><\/b><\/b><\/p>\n

Calculation of the\u00a0<\/span><\/b>apparent frequency\u00a0<\/span><\/b>perceived by the athlete using the\u00a0<\/span><\/b>Doppler effect expression\u00a0<\/span><\/b>f\u00a0<\/b>a<\/b><\/sub>\u00a0= f.(V \u00b1 V\u00a0<\/b>o<\/b><\/sub>\u00a0)\/(V \u00b1 V\u00a0<\/b>F<\/b><\/sub>\u00a0)\u00a0<\/b>f\u00a0<\/b>a<\/b><\/sub>\u00a0=2000(330-3.3)\/(330 \u2013 0)\u00a0<\/b>\u00a0 f\u00a0<\/b>a<\/b><\/sub>\u00a0= 653,400\/330\u00a0\u00a0<\/b>f\u00a0<\/b>a<\/b><\/sub>\u00a0= 1,980 Hz\u00a0\u00a0\u00a0<\/b><\/span>\"\"\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/b>\"\"<\/b>\u00a0<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b>\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b><\/p>\n

Note: You would get the same result if you projected V in the direction of U.<\/span><\/b><\/p>\n

02- (UFJF-MG)\u00a0<\/span><\/b>A\u00a0<\/b>security alarm,\u00a0<\/b>which\u00a0<\/b>is fixed,\u00a0<\/b>is activated, producing a\u00a0<\/b>sound with a frequency of 735 Hz.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

Consider the\u00a0<\/span><\/b>speed of sound in air to be 343 m\/s\u00a0<\/span><\/b>. When a person\u00a0<\/span><\/b>drives a car\u00a0<\/span><\/b>toward\u00a0<\/span><\/b>the alarm\u00a0<\/span><\/b>and then\u00a0<\/span><\/b>away from it at the same speed,\u00a0<\/span><\/b>he observes a\u00a0<\/span><\/b>change in frequency of 78.4 Hz.<\/span><\/b><\/p>\n

a)\u00a0<\/span><\/b>Is\u00a0<\/b>the\u00a0<\/b>frequency heard by the person\u00a0<\/b>when he\u00a0<\/b>approaches the siren\u00a0<\/b>higher or lower than what he would hear if he were standing still? Justify.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

b)\u00a0<\/span><\/b>What is the\u00a0<\/b>speed of the car?<\/b><\/span><\/b><\/b><\/b><\/p>\n

Resolution:<\/span><\/b><\/p>\n

a)\u00a0<\/span><\/b>Greater.\u00a0<\/b>As\u00a0<\/b>the person\u00a0<\/b>approaches the source, he observes an increase in the number of wave fronts passing by him per unit of time\u00a0<\/b>in relation\u00a0<\/b>to the situation in which the person is standing still,\u00a0<\/b>implying\u00a0<\/b>an\u00a0<\/b>increase in frequency.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

b)\u00a0<\/span><\/b>Approaching\u00a0\u00a0<\/span>\"\"<\/b>\u00a0 f\u00a0<\/span><\/b>1<\/span><\/b><\/sub>\u00a0= 735(343+V)\/343\u00a0\u00a0<\/span>\"\"\u00a0\u00a0<\/b>f\u00a0<\/span><\/b>1<\/span><\/b><\/sub>\u00a0= 735 + 2.1V<\/span><\/b><\/p>\n

Moving away\u00a0\u00a0<\/span>\"\"<\/b>\u00a0 f\u00a0<\/span><\/b>2<\/span><\/b><\/sub>\u00a0= 735(343-V)\/343\u00a0\u00a0<\/span>\"\"\u00a0\u00a0<\/b>f\u00a0<\/span><\/b>2<\/span><\/b><\/sub>\u00a0= 735-2.1V<\/span><\/b><\/p>\n

<\/b>The change (variation) of\u00a0<\/span><\/b>frequency\u00a0<\/span><\/b>is given\u00a0<\/b><\/span>\u0394<\/span><\/b><\/span>\u00a0f = 78 Hz \u00a0\u00a0<\/span>\"\"<\/b>\u0394<\/b><\/span>\u00a0f = f\u00a0<\/b>1<\/b><\/sub>\u00a0\u2013 f\u00a0<\/b>2<\/b><\/sub>\u00a0\u00a0 78 = 735 + 2.1V \u2013 (735-2.1V)\u00a0\u00a0<\/b>\u00a0 78 = 735+2.1V \u2013 735 +2.1V\u00a0\u00a0<\/b>V = 18.6 m\/s<\/b><\/span>\u00a0\u00a0\u00a0<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"<\/b>\"\"\"\"\u00a0<\/b><\/b><\/p>\n

03-\u00a0<\/span><\/b>Traveling at a\u00a0\u00a0<\/b>speed of 144 km\/h on a road,\u00a0<\/b>a\u00a0\u00a0<\/b>highway police vehicle\u00a0<\/b>, in pursuit,\u00a0\u00a0<\/b>sounds the siren, the sound of which has a frequency equal to 1500 Hz\u00a0<\/b>.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

A\u00a0\u00a0<\/span><\/b>woman standing\u00a0\u00a0<\/span><\/b>at a point<\/span><\/b>\"\"<\/p>\n

by bus, on the same road,\u00a0<\/span><\/b>notices a sudden variation in the sound, at the moment the vehicle passes the point where she is. What is\u00a0<\/span><\/b>the approximate\u00a0\u00a0<\/span><\/b>frequency variation, in Hz, heard by the woman,\u00a0<\/span><\/b>taking as a parameter the\u00a0<\/span><\/b>periods before and after the vehicle passes?<\/span><\/b><\/p>\n

Adopt the\u00a0<\/span><\/b>speed of sound V\u00a0<\/span><\/b>s<\/span><\/b><\/sub>\u00a0\u00a0= 340 m\/s<\/span><\/b><\/p>\n

Resolution:<\/span><\/b><\/p>\n

Source approaching woman\u00a0<\/span><\/b>f\u00a0<\/b>a<\/b><\/sub>\u00a0= 1500(340 + 0)\/(340 \u2013 40)\u00a0<\/b>= 1500.340\/300\u00a0<\/b>f\u00a0<\/b>a<\/b><\/sub>\u00a0= 1700Hz<\/b><\/span>\u00a0\"\"\u00a0<\/b><\/b><\/b><\/b>\"\"\u00a0<\/b><\/b><\/b><\/b><\/p>\n

Source moving away from woman\u00a0<\/span><\/b>f\u00a0<\/b>a<\/b><\/sub>\u00a0= 1500(340 + 0)\/(340 +40)\u00a0<\/b>= 1500.340\/380\u00a0<\/b>f\u00a0<\/b>a<\/b><\/sub>\u00a0= 1342.6Hz<\/b><\/span>\u00a0\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b>\"\"\u00a0<\/b><\/b><\/b><\/b><\/p>\n

\u0394f\u00a0<\/span><\/b>= 1700 \u2013 1342\u00a0<\/span><\/b>= 358Hz.<\/span><\/b><\/p>\n

 <\/p>\n

03- (ITA-SP)\u00a0<\/span><\/b>A\u00a0<\/span><\/b>young woman sits on the seat of a circular carousel\u00a0<\/span><\/b>that\u00a0<\/span><\/b>rotates at a speed<\/span><\/b><\/p>\n

constant angular with period T.<\/span><\/b>\"\"<\/p>\n

A\u00a0<\/span><\/b>siren positioned outside the carousel\u00a0<\/span><\/b>emits a\u00a0<\/span><\/b>sound of frequency f\u00a0<\/span><\/b>o<\/span><\/b><\/sub>\u00a0\u00a0towards the center of rotation.<\/span><\/b><\/p>\n

At\u00a0<\/span><\/b>time t = 0, the young woman is at the shortest distance from\u00a0<\/span><\/b>the\u00a0<\/span><\/b>siren.\u00a0<\/span><\/b><\/p>\n

In this situation,\u00a0<\/span><\/b>indicate the best representation of the frequency f heard by the young woman.<\/span><\/b><\/p>\n

\"\"<\/p>\n

Observe the diagram in the\u00a0<\/span><\/b>figure below:<\/span><\/b><\/p>\n

\"\"\u00a0At\u00a0<\/span><\/b>instant t = 0 the young woman\u00a0<\/span><\/b>(listener or observer) is in the\u00a0<\/span><\/b>position shown in the figure\u00a0\u00a0<\/span>\"\"<\/b>\u00a0\u00a0at this point, the\u00a0<\/span><\/b>frequency heard (f\u00a0<\/span><\/b>)\u00a0<\/span><\/b>is equal to the frequency of the siren (f\u00a0<\/span><\/b>o<\/span><\/b><\/sub>\u00a0)\u00a0<\/span><\/b>\u201creceives the same amount of waves as those emitted by the siren, even \u03bb\u201d such that\u00a0<\/span><\/b>f\/f\u00a0<\/span><\/b>o<\/span><\/b><\/sub>\u00a0= 1 (f = f\u00a0<\/span><\/b>o<\/span><\/b><\/sub>\u00a0).<\/span><\/b>\"\"<\/p>\n

\"\"\u00a0From\u00a0<\/span><\/b>that moment on,\u00a0<\/b><\/span>until\u00a0<\/span><\/b>T\/2, there is a relative distance between the young woman and the siren,\u00a0<\/b>so that the\u00a0<\/b>frequency heard by her is lower than the frequency emitted by the siren f\/f\u00a0<\/b>o<\/b><\/sub>\u00a0<1 (f < f\u00a0<\/b>o<\/b><\/sub>\u00a0).<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

\"\"\u00a0at instant t = T\/2,\u00a0<\/span><\/b>it\u00a0<\/span><\/b>hears the frequency emitted by the source again\u00a0\u00a0<\/span><\/b>(it receives the same amount of waves as those emitted by the siren, even \u03bb) such that\u00a0<\/span><\/b>f\/f\u00a0<\/span><\/b>o<\/span><\/b><\/sub>\u00a0= 1 (f = f\u00a0<\/span><\/b>o<\/span><\/b><\/sub>\u00a0).<\/span><\/b><\/p>\n

\"\"\u00a0From\u00a0<\/span><\/b>T\/2 to T,\u00a0<\/span><\/b>there is\u00a0<\/span><\/b>a relative approximation between the young woman and the siren and she begins to perceive a frequency higher than that emitted by the siren f\/f\u00a0<\/span><\/b>o<\/span><\/b><\/sub>\u00a0> 1 (f > f\u00a0<\/span><\/b>o<\/span><\/b><\/sub>\u00a0).<\/span><\/b><\/p>\n

Note that\u00a0<\/span><\/b>the maximum speeds of separation and approach occur at t = T\/4 and at t = 3T\/4,\u00a0<\/span><\/b>instants at\u00a0<\/span><\/b>which<\/b><\/sub><\/span>\u00a0f\/f\u00a0<\/span><\/b>reaches\u00a0<\/b>minimum and maximum values, respectively\u00a0<\/b>R- A<\/b><\/span><\/b><\/b><\/b>\u00a0\"\"\u00a0\u00a0<\/b><\/b><\/p>\n

Check out the exercises<\/span><\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

Doppler effect It refers to the\u00a0variation in frequency noticed\u00a0by an\u00a0observer\u00a0when the\u00a0distance between him and a wave source is increasing or decreasing. When\u00a0the source and observer come closer together,\u00a0the\u00a0latter will perceive the sound emitted by the source as higher pitched\u00a0(higher frequency, receives a greater number of wave fronts in the unit of time) than\u00a0it would perceive if the source and observer<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2325,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-11676","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11676","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/comments?post=11676"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11676\/revisions"}],"predecessor-version":[{"id":12066,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11676\/revisions\/12066"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2325"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=11676"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}