{"id":11678,"date":"2024-11-28T15:11:26","date_gmt":"2024-11-28T15:11:26","guid":{"rendered":"https:\/\/fisicaevestibular.com.br\/novo\/?page_id=11678"},"modified":"2024-12-03T14:15:38","modified_gmt":"2024-12-03T14:15:38","slug":"ondas-estacionarias-en","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/ondulatoria\/acustica\/ondas-estacionarias-en\/","title":{"rendered":"Standing Waves – EN"},"content":{"rendered":"

Standing Waves<\/span><\/b><\/p>\n

Formation of standing waves<\/span><\/b><\/p>\n

We obtain\u00a0\u00a0<\/span><\/b>standing waves\u00a0<\/span><\/b>\u00a0by\u00a0<\/span><\/b>superposing two identical waves,\u00a0<\/span><\/b>of\u00a0<\/span><\/b>the same amplitude, same frequency, same wavelength\u00a0<\/span><\/b>and that\u00a0<\/span><\/b>move in the same direction and opposite directions.<\/span><\/b><\/p>\n

Consider a\u00a0<\/span><\/b>string fixed at\u00a0<\/span><\/b>one\u00a0<\/span><\/b>end and\u00a0<\/span><\/b>a source producing periodic waves\u00a0<\/b><\/span>at the other.<\/span><\/b><\/b><\/b><\/p>\n

which, upon\u00a0<\/span><\/b>reaching the fixed end,\u00a0<\/span><\/b>undergo reflection and return.<\/b><\/span><\/b><\/b><\/b><\/p>\n

Thus, the\u00a0<\/span><\/b>incident and reflected waves\u00a0<\/span><\/b>superimpose\u00a0<\/span><\/b>,\u00a0<\/span><\/b>creating\u00a0<\/span><\/b>standing waves.<\/b><\/span><\/b><\/b><\/p>\n

To\u00a0<\/span><\/b>understand\u00a0<\/span><\/b>how\u00a0<\/span><\/b>standing waves arise\u00a0<\/span><\/b>, carefully observe the sequences of\u00a0<\/span><\/b>figures below,\u00a0<\/span><\/b>where,\u00a0<\/span><\/b>in all of\u00a0<\/span><\/b>them,\u00a0<\/span><\/b>at the same time\u00a0<\/span><\/b>, in the\u00a0<\/span><\/b>two figures on the left,\u00a0<\/span><\/b>we have\u00a0<\/span><\/b>waves\u00a0<\/span><\/b>moving in opposite directions\u00a0<\/b>and, in the\u00a0<\/b>figure on the right, their superposition, at the same time.<\/b><\/span><\/b><\/b><\/b><\/b>\"\"<\/p>\n

The\u00a0<\/span><\/b>time interval between one figure and another is a quarter of a period (T\/4),\u00a0<\/span><\/b>that is,\u00a0<\/span><\/b>between each interval the wave traveled a quarter of a wavelength.<\/span><\/b><\/p>\n

At\u00a0<\/span><\/b>time t = 0,\u00a0<\/span><\/b>the\u00a0<\/span><\/b>two waves are exactly superimposed and the wave resulting from this superposition has amplitude 2A. (constructive interference).<\/span><\/b><\/p>\n

\"\"<\/p>\n

At\u00a0<\/span><\/b>time t = T\/4,\u00a0<\/span><\/b>each\u00a0<\/b>of them\u00a0<\/b>has moved \u03bb\/4 and their configurations are shown in the two figures on the\u00a0<\/b>left.\u00a0<\/b>Note, in the\u00a0<\/b>figure on the right, that all the points of these waves cancel each other out (destructive interference).<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

At\u00a0<\/span><\/b>time t = T\/2,\u00a0<\/span><\/b>the resulting wave\u00a0<\/span><\/b>has amplitude 2A.<\/span><\/b><\/p>\n

\"\"<\/p>\n

At\u00a0<\/span><\/b>time t = 3T\/2\u00a0<\/span><\/b>these waves\u00a0<\/span><\/b>cancel each other out again.<\/span><\/b><\/p>\n

At\u00a0<\/span><\/b>instant t=T\u00a0<\/span><\/b>, these waves\u00a0<\/span><\/b>returned to the initial situation\u00a0<\/span><\/b>and from\u00a0<\/span><\/b>then on the repetition begins.<\/span><\/b>\"\"<\/p>\n

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Note that at\u00a0<\/span><\/b>all instants,\u00a0<\/span><\/b>points\u00a0<\/span><\/b>P, Q and R\u00a0<\/span><\/b>of the\u00a0<\/span><\/b>resulting wave did not move.\u00a0<\/span><\/b>These points, which\u00a0<\/b>are always fixed,\u00a0<\/b>are called\u00a0\u00a0<\/b>nodes\u00a0<\/b>\u00a0and are in\u00a0<\/b>destructive interference.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

Also note that at\u00a0<\/span><\/b>all instants,\u00a0<\/span><\/b>all\u00a0<\/b>points\u00a0<\/b>between P and Q and between Q and<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/p>\n

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Each\u00a0<\/span><\/b>of these\u00a0<\/span><\/b>amplitudes is twice the amplitudes\u00a0<\/span><\/b>of the\u00a0<\/span><\/b>constituent waves.<\/span><\/b><\/p>\n

Since the\u00a0<\/span><\/b>nodes are at rest,\u00a0<\/span><\/b>there can be no passage of energy through them\u00a0<\/b>,\u00a0<\/b>meaning that there is no\u00a0<\/b>energy transport\u00a0<\/b>in a\u00a0<\/b>stationary rope .<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

Thus,\u00a0<\/span><\/b>standing waves\u00a0<\/span><\/b>are not propagating waves,\u00a0<\/b>but rather the\u00a0<\/b>different ways in which a string, membrane, etc. vibrates.<\/b><\/span><\/b><\/b><\/b><\/b><\/p>\n

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Sound interference<\/span><\/b><\/p>\n

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It occurs when\u00a0<\/span><\/b>two or more sound waves\u00a0<\/span><\/b>overlap\u00a0<\/span><\/b>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>\u00a0= 100 Hz\u00a0<\/span><\/b>and the other of\u00a0<\/span><\/b>f\u00a0<\/span><\/b>B<\/span><\/b><\/sub>\u00a0= 110 Hz.<\/span><\/b><\/p>\n

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

\"\"<\/p>\n

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

The\u00a0<\/span><\/b>beat frequency is defined\u00a0<\/span><\/b>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\u00a0<\/span><\/b>used in the tuning of musical instruments.<\/span><\/b><\/b><\/p>\n

If the\u00a0<\/span><\/b>frequencies of the sharpening source and the instrument are different, the beat is heard.<\/span><\/b><\/b><\/p>\n

The\u00a0<\/span><\/b>frequency of the beat decreases\u00a0<\/span><\/b>as\u00a0<\/span><\/b>the instrument is tuned\u00a0<\/span><\/b>, and when\u00a0<\/span><\/b>it disappears,\u00a0<\/span><\/b>the\u00a0<\/span><\/b>instrument is in tune.<\/span><\/b><\/p>\n

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

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Each\u00a0<\/span><\/b>of the\u00a0<\/span><\/b>amplitudes of the standing wave\u00a0<\/span><\/b>is\u00a0<\/span><\/b>twice the amplitudes of the constituent waves.<\/span><\/b><\/p>\n

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Since\u00a0<\/span><\/b>the nodes are at rest, there\u00a0<\/span><\/b>can be\u00a0<\/b>no\u00a0<\/b>passage of energy through them,\u00a0<\/b>meaning that there is no\u00a0<\/b>energy transport\u00a0<\/b>in a standing wave.<\/b><\/span>\u00a0<\/b><\/b><\/b><\/b>\u00a0<\/b><\/b><\/b><\/b><\/p>\n

Thus,\u00a0<\/span><\/b>standing waves are not propagating waves\u00a0<\/span><\/b>, but rather the\u00a0<\/span><\/b>different ways in which a string, membrane, etc. vibrates.<\/span><\/b><\/p>\n\n\n<\/colgroup>\n\n\n
<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

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The\u00a0<\/span><\/b>beat frequency is defined\u00a0<\/span><\/b>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

\"\"<\/p>\n

The\u00a0<\/span><\/b>phenomenon of beating\u00a0<\/span><\/b>is often\u00a0<\/span><\/b>used in the tuning of musical instruments.<\/span><\/b><\/b><\/p>\n

If the\u00a0<\/span><\/b>frequencies of the sharpening source and the instrument are different, the beat is heard.<\/span><\/b><\/b><\/p>\n

The\u00a0<\/span><\/b>frequency of the beat decreases\u00a0<\/span><\/b>as\u00a0<\/span><\/b>the instrument is tuned\u00a0<\/span><\/b>, and when\u00a0<\/span><\/b>it disappears,\u00a0<\/span><\/b>the\u00a0<\/span><\/b>instrument is in tune.<\/span><\/b><\/p>\n

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Formulas<\/span><\/b><\/p>\n

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Some interesting exercises in which you might want to analyze the resolutions:<\/span><\/b><\/p>\n

\"\"<\/p>\n

02- (UFMS)\u00a0<\/span><\/b>The figure shows\u00a0<\/b>standing waves\u00a0<\/b>in a\u00a0<\/b>string of length 45 cm,\u00a0<\/b>with\u00a0<\/b>linear mass density \u03bc = 6.2 g\/m,\u00a0<\/b>with both\u00a0<\/b>ends fixed,\u00a0<\/b>and which is\u00a0<\/b>vibrating at 450 Hz.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

Give as\u00a0<\/span><\/b>your answer the sum of the numbers corresponding to the correct statements.<\/span><\/b><\/p>\n

It is\u00a0<\/span><\/b>correct to state\u00a0<\/span><\/b>that:<\/span><\/b><\/p>\n

(01)\u00a0<\/span><\/b>all points\u00a0<\/b>of the string\u00a0<\/b>vibrate\u00a0<\/b>with the\u00a0<\/b>same amplitude.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

(02)\u00a0<\/span><\/b>all points\u00a0<\/b>of the string\u00a0<\/b>vibrate\u00a0<\/b>at the\u00a0<\/b>same frequency.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

(04)\u00a0<\/span><\/b>the\u00a0<\/span><\/b>wavelength\u00a0<\/span><\/b>on the string is\u00a0<\/span><\/b>90 cm.<\/span><\/b>\"\"<\/p>\n

(08)\u00a0<\/span><\/b>the\u00a0<\/span><\/b>wave\u00a0<\/b><\/span>propagation speed in the rope is\u00a0<\/span><\/b>135 m\/s.<\/b><\/span><\/b><\/b><\/p>\n

(16)\u00a0<\/span><\/b>the\u00a0<\/span><\/b>tension force\u00a0<\/span><\/b>on the rope is approximately\u00a0<\/span><\/b>113N\u00a0<\/span><\/b>.<\/span><\/b><\/p>\n

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

(01)\u00a0<\/span><\/b>Wrong.\u00a0<\/b>The\u00a0<\/b>movement of each point of the standing wave is only\u00a0<\/b>vertical\u00a0<\/b>and check in the\u00a0<\/b>figure below\u00a0<\/b>that\u00a0<\/b>points A, A1\u00a0<\/b>and<\/b><\/sub>\u00a0\u00a0A2\u00a0<\/b>have<\/b><\/sub>\u00a0different\u00a0<\/b>amplitudes in their complete \u201cup and down\u201d.<\/b><\/span>\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b>\u00a0<\/b>\u00a0<\/b><\/sub><\/b><\/b><\/p>\n

\"\"<\/p>\n

(02)\u00a0<\/span><\/b>Correct.\u00a0<\/b>This\u00a0<\/b>frequency of 450Hz\u00a0<\/b>is the\u00a0<\/b>frequency of the waves that superimpose\u00a0<\/b>and is the same\u00a0<\/b>for all points of the string that vibrate.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

(04)\u00a0<\/span><\/b>Wrong.\u00a0<\/b>3\u03bb\/2 = 45\u00a0<\/b>\u03bb = 30 cm.<\/b><\/span>\u00a0<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b><\/p>\n

(08)\u00a0<\/span><\/b>Correct.\u00a0<\/b>V = \u03bbf\u00a0<\/b>V\u00a0<\/b>= 30,450 =\u00a0<\/b>13,500 cm\/s = 135 m\/s.<\/b><\/span>\u00a0<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0<\/b><\/b><\/b><\/b><\/p>\n

(16)\u00a0<\/span><\/b>Correct.\u00a0<\/b>V=\u221a(F\/\u03bc)\u00a0<\/b>\u00a0 135 = \u221a(F\/6.2.10\u00a0<\/b>-3<\/b><\/sup>\u00a0)\u00a0\u00a0<\/b>\u00a0 (135)\u00a0<\/b>2<\/b><\/sup>\u00a0= (F\/6.2.10\u00a0<\/b>-3<\/b><\/sup>\u00a0)\u00a0<\/b>2<\/b><\/sup>\u00a0\u00a0 18.225 = F\/0.0062\u00a0\u00a0<\/b><\/span><\/b><\/b>\u00a0\u00a0<\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b>\"\"<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\"\"\u00a0<\/b><\/p>\n

F = 112.995 N.<\/span><\/b><\/p>\n

Sum = (02 + 08 +16) = 26<\/span><\/b><\/p>\n

\"\"<\/p>\n

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

Applying the\u00a0<\/span><\/b>fundamental wave equation\u00a0<\/span><\/b>to:<\/b><\/span>\u00a0<\/b><\/b><\/b><\/p>\n

City radio\u00a0<\/span><\/b>V =\u00a0<\/b>\u03bb\u00a0<\/b><\/span>c<\/b><\/sub>\u00a0.f\u00a0<\/b>c<\/b><\/sub>\u00a0. \u00a0<\/b><\/span>\u00a0\u00a0\"\"\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

Pirate radio\u00a0<\/span><\/b>V =\u00a0<\/b>\u03bb\u00a0<\/b><\/span>p<\/b><\/sub>\u00a0.f\u00a0<\/b>p<\/b><\/sub>\u00a0.\u00a0<\/b><\/span>\u00a0\u00a0\"\"\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

As the\u00a0<\/span><\/b>speed (V) of wave propagation is the same,\u00a0<\/span><\/b>as it is\u00a0<\/span><\/b>the same propagation medium (air),\u00a0<\/span><\/b>and the\u00a0<\/span><\/b>frequencies (f), according to the statement, are the same\u00a0<\/span><\/b>, the\u00a0<\/span><\/b>wavelengths (\u03bb) will also be the same.<\/span><\/b><\/p>\n

R- And<\/span><\/b><\/p>\n

\"\"<\/p>\n

Resolution:\u00a0<\/span><\/b><\/p>\n

Point\u00a0<\/span><\/b>2 on the string is a node\u00a0<\/span><\/b>of the\u00a0<\/span><\/b>standing wave\u00a0<\/span><\/b>and\u00a0<\/span><\/b>remains fixed\u00a0<\/span><\/b>\u00a0.<\/span><\/b><\/p>\n

Points\u00a0<\/span><\/b>1 and 3\u00a0<\/span><\/b>have\u00a0<\/span><\/b>zero speed\u00a0<\/span><\/b>at the upper and lower ends\u00a0<\/span><\/b>and\u00a0<\/span><\/b>maximum\u00a0<\/b><\/span>speeds\u00a0<\/span><\/b>when\u00a0<\/b>they pass through the center\u00a0<\/b>(where these points are),\u00a0\u00a0<\/b>but they\u00a0<\/b>have speeds in opposite directions,\u00a0<\/b>that is, while one\u00a0<\/b>is going up the other will be going down.<\/b><\/span><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

R-D.<\/span><\/b><\/p>\n

\"\"<\/p>\n

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

Observe in the\u00a0<\/span><\/b>figures below the standing waves\u00a0<\/span><\/b>formed in\u00a0<\/span><\/b>each case:<\/span><\/b><\/p>\n

First figure\u00a0<\/span><\/b>\u03bb\u00a0<\/b>1<\/b><\/sub>\u00a0\/2 = L\u00a0<\/b>\u00a0 \u03b3\u00a0<\/b>1<\/b><\/sub>\u00a0= 2L\u00a0\u00a0<\/b>\u00a0 V\u00a0<\/b>1<\/b><\/sub>\u00a0= \u03b3\u00a0<\/b>1<\/b><\/sub>\u00a0.f\u00a0<\/b>1<\/b><\/sub>\u00a0V\u00a0<\/b>1<\/b><\/sub>\u00a0= 2L.f\u00a0<\/b>1<\/b><\/sub>\u00a0(I).<\/b><\/span>\u00a0\"\"\u00a0<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b>\"\"<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/p>\n

\"\"<\/p>\n

Second figure\u00a0<\/span><\/b>\u03b3\u00a0<\/b>2<\/b><\/sub>\u00a0\/2 = L\/2\u00a0<\/b>\u03b3\u00a0<\/b>2<\/b><\/sub>\u00a0= L\u00a0<\/b>V\u00a0<\/b>2<\/b><\/sub>\u00a0= \u03b3\u00a0<\/b>2<\/b><\/sub>\u00a0.f\u00a0<\/b>2<\/b><\/sub>\u00a0V\u00a0<\/b>2<\/b><\/sub>\u00a0= Lf\u00a0<\/b>2<\/b><\/sub>\u00a0\u00a0(II).<\/b><\/span>\u00a0\"\"\u00a0<\/b><\/b><\/b><\/b>\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0<\/b><\/p>\n

Since the\u00a0<\/span><\/b>propagation speed in each case is the same\u00a0<\/span><\/b>(same medium, air)\u00a0\u00a0<\/span>\"\"\u00a0\u00a0<\/b>V\u00a0<\/span><\/b>1<\/span><\/b><\/sub>\u00a0= V\u00a0<\/span><\/b>2<\/span><\/b><\/sub>\u00a0I = II\u00a0<\/b>2Lf\u00a0<\/b>1<\/b><\/sub>\u00a0= Lf\u00a0<\/b>2<\/b><\/sub>\u00a0\u00a0 \u2014 2,220 = f\u00a0<\/b>2<\/b><\/sub>\u00a0f\u00a0<\/b>2<\/b><\/sub>\u00a0= 440 Hz.\u00a0<\/b><\/span>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b>\u00a0\u00a0\"\"<\/b><\/b><\/b><\/b><\/b><\/b>\u00a0\u00a0\"\"\u00a0\u00a0<\/b><\/b><\/b><\/b>\u00a0\u00a0<\/b><\/p>\n

A- A<\/span><\/b><\/p>\n

 <\/p>\n

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

Standing Waves Formation of standing waves We obtain\u00a0\u00a0standing waves\u00a0\u00a0by\u00a0superposing two identical waves,\u00a0of\u00a0the same amplitude, same frequency, same wavelength\u00a0and that\u00a0move in the same direction and opposite directions. Consider a\u00a0string fixed at\u00a0one\u00a0end and\u00a0a source producing periodic waves\u00a0at the other. which, upon\u00a0reaching the fixed end,\u00a0undergo reflection and return. Thus, the\u00a0incident and reflected waves\u00a0superimpose\u00a0,\u00a0creating\u00a0standing waves. To\u00a0understand\u00a0how\u00a0standing waves arise\u00a0, carefully observe the sequences of\u00a0figures below,\u00a0where,\u00a0in<\/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-11678","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11678","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=11678"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11678\/revisions"}],"predecessor-version":[{"id":12067,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/11678\/revisions\/12067"}],"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=11678"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}