Answer
64.8k+ views
Hint: If the frequency when the car is approaching is \[{f_1}\] and when the car is leaving is \[{f_2}\]. Get the value of \[{f_1}\] and \[{f_2}\] in terms of \[{f_0}\] . The Doppler effect or Doppler shift can be describing the changes in frequency of sound or light wave produced by a moving source with respect to an observer. Also, we know that the beat frequency is defined as the difference in frequency of two waves. By using this we can get the result.
Formula used:
Frequency when source is approaching is given as,
\[{f_1} = {f_0}\left( {\dfrac{v}{{v - {v_0}}}} \right)\]
Frequency when source is leaving is given as,
\[{f_2} = {f_0}\left( {\dfrac{v}{{v + {v_0}}}} \right)\]
Where \[{f_1}\] and \[{f_2}\] is the frequency required, \[{f_0}\] is the given frequency, \[v\] is the velocity of the observer and \[{v_0}\] is the velocity of sound.
Beat frequency is given as,
\[{f_1} - {f_2}\]
Where \[{f_1} - {f_2}\] represents the change in frequency.
Complete step by step solution:
As we know that the frequency when source is approaching is given as,
\[{f_1} = {f_0}\left( {\dfrac{v}{{v - {v_0}}}} \right) \\ \]
Frequency when source is leaving is given as,
\[{f_2} = {f_0}\left( {\dfrac{v}{{v + {v_0}}}} \right) \\ \]
Now the beat frequency = \[{f_1} - {f_2} \\ \]
\[\text{beat frequency} = {f_0}v\left( {\dfrac{1}{{v - {v_0}}} - \dfrac{1}{{v + {v_0}}}} \right) \\ \]
\[\Rightarrow \text{beat frequency} = {f_0}v\left( {\dfrac{{v + {v_0} - v + {v_0}}}{{{v^2} - v_0^2}}} \right) \\ \]
\[\therefore \text{beat frequency} = \dfrac{{2{f_0}v{v_0}}}{{{v^2} - v_0^2}}\]
Hence option C is the correct answer.
Note:The formula for Doppler Effect is related to the frequency of the sound of an object with its velocity. Doppler Effect is defined as the change in wave frequency during the relative motion between the wave source and its observer. It was given by Christian Johann Doppler. Beats can be determined by subtracting the initial frequency with the frequency observed by the observer.
Formula used:
Frequency when source is approaching is given as,
\[{f_1} = {f_0}\left( {\dfrac{v}{{v - {v_0}}}} \right)\]
Frequency when source is leaving is given as,
\[{f_2} = {f_0}\left( {\dfrac{v}{{v + {v_0}}}} \right)\]
Where \[{f_1}\] and \[{f_2}\] is the frequency required, \[{f_0}\] is the given frequency, \[v\] is the velocity of the observer and \[{v_0}\] is the velocity of sound.
Beat frequency is given as,
\[{f_1} - {f_2}\]
Where \[{f_1} - {f_2}\] represents the change in frequency.
Complete step by step solution:
As we know that the frequency when source is approaching is given as,
\[{f_1} = {f_0}\left( {\dfrac{v}{{v - {v_0}}}} \right) \\ \]
Frequency when source is leaving is given as,
\[{f_2} = {f_0}\left( {\dfrac{v}{{v + {v_0}}}} \right) \\ \]
Now the beat frequency = \[{f_1} - {f_2} \\ \]
\[\text{beat frequency} = {f_0}v\left( {\dfrac{1}{{v - {v_0}}} - \dfrac{1}{{v + {v_0}}}} \right) \\ \]
\[\Rightarrow \text{beat frequency} = {f_0}v\left( {\dfrac{{v + {v_0} - v + {v_0}}}{{{v^2} - v_0^2}}} \right) \\ \]
\[\therefore \text{beat frequency} = \dfrac{{2{f_0}v{v_0}}}{{{v^2} - v_0^2}}\]
Hence option C is the correct answer.
Note:The formula for Doppler Effect is related to the frequency of the sound of an object with its velocity. Doppler Effect is defined as the change in wave frequency during the relative motion between the wave source and its observer. It was given by Christian Johann Doppler. Beats can be determined by subtracting the initial frequency with the frequency observed by the observer.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Other Pages
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Electric field due to uniformly charged sphere class 12 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
According to classical free electron theory A There class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)