డాప్లర్ ప్రభావం: కూర్పుల మధ్య తేడాలు
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గణిత సమీకరణాన్ని జత పరుస్తున్నాను. |
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పంక్తి 11:
[[దస్త్రం:Speeding-car-horn doppler effect sample.ogg|thumbnail|డాప్లర్ ప్రభావం గురించి తెలియజేస్తున్న ఆడియో]]
[[దస్త్రం:Doppler heartbeat 0218103423 1038270 7w 3d.gif|thumbnail|కుడి|డాప్లర్ అల్ట్రా సౌండ్ ను ఉపయోగించి హార్ట్ బీట్ ను కనుగొనవచ్చును.]]
==గణిత సమీకరణం==
In classical physics, where the speeds of source and the receiver relative to the medium are lower than the velocity of waves in the medium, the relationship between observed frequency <math>f</math> and emitted frequency <math>f_\text{0}</math> is given by:<ref name=encphysci>{{cite book
|title=Encyclopedia of Physical Science
|first1=Joe
|last1=Rosen
|first2=Lisa Quinn
|last2=Gothard
|publisher=Infobase Publishing
|date=2009
|isbn=0-8160-7011-3
|page=155
|url=https://books.google.com/books?id=avyQ64LIJa0C}} [https://books.google.com/books?id=avyQ64LIJa0C&pg=PA155 Extract of page 155]</ref>
::<math>f = \left( \frac{c + v_\text{r}}{c + v_\text{s}} \right) f_0 \,</math>
:where
::<math>c \;</math> is the velocity of waves in the medium;
::<math>v_\text{r} \,</math> is the velocity of the receiver relative to the medium; positive if the receiver is moving towards the source (and negative in the other direction);
::<math>v_\text{s} \,</math> is the velocity of the source relative to the medium; positive if the source is moving away from the receiver (and negative in the other direction).
The frequency is decreased if either is moving away from the other.
The above formula assumes that the source is either directly approaching or receding from the observer. If the source approaches the observer at an angle (but still with a constant velocity), the observed frequency that is first heard is higher than the object's emitted frequency. Thereafter, there is a [[monotonic]] decrease in the observed frequency as it gets closer to the observer, through equality when it is coming from a direction perpendicular to the relative motion (and was emitted at the point of closest approach; but when the wave is received, the source and observer will no longer be at their closest), and a continued monotonic decrease as it recedes from the observer. When the observer is very close to the path of the object, the transition from high to low frequency is very abrupt. When the observer is far from the path of the object, the transition from high to low frequency is gradual.
If the speeds <math>v_\text{s} \,</math> and <math>v_\text{r} \,</math> are small compared to the speed of the wave, the relationship between observed frequency <math>f</math> and emitted frequency <math>f_\text{0}</math> is approximately<ref name=encphysci />
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==అనువర్తనాలు==
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