Verification of the third condition of the Doppler effect (receiver and transmitter of moving sound) (ENG-ESP)

[rbalzan79]

Greetings again my dear friends I hope you are all very well, this time we will analyze the third condition of the Doppler effect, remember that in the first condition, the receiver was motionless and the sound emission focus in motion, in the second condition the receiver was in motion and the sound emission focus motionless, now in the third condition both are in motion, and for this, we will use again the general formulation of the Doppler effect, which is adapted to this third condition.

Therefore, let us now describe the following practical exercise.

Exercise

A young man is moving on his skateboard at a speed of 6 km / h, and does so in the opposite direction to the direction of a fire truck, whose speed is 100 km / h, the truck emits its particular emergency sound at a frequency of 3,200 Hz, this sound, of course, uses as a material medium of propagation to the air, where, it moves at a speed of 340 m / s. In relation to the above described answer the following question:

a.-What would be the frequencies perceived by the youngster on the skateboard, and what do these frequencies indicate to us by linking them to the frequency of the emitting source?

Solution

a.- First of all, it is important to point out the general formula of the Doppler effect:

fr = It is the frequency of the sound perceived by the receiver.
fo = Represents the sound frequency of the emitting source.
Vm = Velocity of the sound propagation medium (air in this case)
VR = Receiver speed.
Vf = Speed of the sound emitting source.

For this third condition, this formula fits adequately, since both binding elements are in motion, we would only have to consider the use of the signs, which you will see later on, therefore, we can start with.

Data:

VR = 5 km/h * 1 h/3600 s * 1000 m/km = 1,39 m/s.
Vf = 100 km/h * 1 h/3600 s * 1000 m/km = 27,78 m/s.
fo = 3.200 Hz.
Vm = 340 m/s.

As we have expressed for this third condition, both the receiver and the emitter of sound are in motion, so both elements have speed, so in this opportunity we will consider the positive signs (+) when both mobiles are moving away, and the negative signs (-) when both mobiles are approaching, and having all this clear we can continue giving solution to this question.

This is the frequency of the sound perceived by the receiver when the two are moving away from each other, because they are going in opposite directions.

Now let's see what happens when both mobiles approach each other, expressing the formulation with negative sign (-) as you can see.

This is the frequency of the sound perceived by the receiver when the two mobiles approach each other.

Analysis of results

For this third condition of the Doppler effect, which indicates that both mobiles are in motion, that is, both the receiver and the emitter of the sound, and according to the calculations made, we continue to notice the same characteristics of this particular physical phenomenon, which makes the frequency perceived by the receiver different from that emitted by the source emitting the sound (ambulance).

This characteristic was verified in the same way when both mobiles approached and moved away from each other, so that this principle is fulfilled for the three conditions analyzed:

First condition: Receiver immobile, and sound emitting focus in motion.

Second condition: Receiver in motion, and sound emitter immobile.

Third condition: Receiver and emitter of sound, both in motion.

For these three conditions, the receiver of the sound perceived a frequency different from the frequency emitted by the sound emitting source, both when approaching and when moving away. In the following table you will observe the frequency ratios for this third condition.

You can see the previous articles related to the first two conditions analyzed in the following links:

1.- Doppler effect, stationary receiver.

2.- Doppler effect, moving receiver and stationary transmitter.

Until another opportunity my dear friends.

Note: The images were created by the author using Power Point and Paint.

Recommended Bibliographic References

[1] MOVIMIENTO ONDULATORIO. Link.

[2] Doppler Effect. Link.

Saludos de nuevo mis queridos amigos espero que se encuentren todos muy bien, en esta oportunidad analizaremos la tercera condición del efecto Doppler, recordemos que, en la primera, el receptor estaba inmóvil y el foco de emisión de sonido en movimiento, en la segunda se encontraba en movimiento el receptor y el foco de emisión de sonido inmóvil, ahora en la tercera condición ambos están en movimiento, y para ello, utilizaremos nuevamente la formulación general del efecto Doppler, la cual se adapta a esta tercera condición.

Por lo tanto, pasemos a describir el siguiente ejercicio práctico.

Ejercicio

Un joven se desplaza en su patineta a una velocidad de 6 km/h, y lo hace en sentido contrario a la dirección de un camión de bomberos, cuya velocidad es de 100 km/h, el camión emite su particular sonido de emergencia a una frecuencia de 3.200 Hz, este sonido, por supuesto, utiliza como medio material de propagación al aire, donde, se desplaza a una velocidad de 340 m/s. En relación a lo antes descrito responder a la siguiente interrogante:

a.- ¿Cuáles serían las frecuencias percibidas por el joven en la patineta, y que nos indican estas frecuencias al vincularlas con la frecuencia del foco emisor?

Solución

a.-En primer lugar, es importante señalar la fórmula general del efecto Doppler:

fr = Es la frecuencia del sonido percibida por el receptor.
fo = Representa la frecuencia del sonido del foco emisor.
Vm = Velocidad del medio de propagación del sonido (El aire en este caso)
VR = Velocidad del receptor.
Vf = Velocidad del foco emisor del sonido.

Para esta tercera condición, dicha fórmula se ajusta adecuadamente, ya que, ambos elementos vinculantes se encuentran en movimiento, solo tendríamos que considerar el uso de los signos lo cual podrán ver más adelante, por lo tanto, podemos iniciar.

Datos:

VR = 5 km/h * 1 h/3600 s * 1000 m/km = 1,39 m/s.
Vf = 100 km/h * 1 h/3600 s * 1000 m/km = 27,78 m/s.
fo = 3.200 Hz.
Vm = 340 m/s.

Como hemos expresado para esta tercera condición, tanto el receptor como el emisor de sonido están en movimiento, por lo que ambos elementos poseen velocidad, por lo que en esta oportunidad consideraremos los signos positivos (+) cuando ambos móviles se alejan, y los signos negativos (-) cuando ambos móviles se acercan, ya teniendo claro todo esto podemos seguir dándole solución a esta interrogante.

Esta es la frecuencia del sonido percibido por el receptor cuando ambos se alejan entre sí, debido a que van en sentido opuesto.

Ahora veamos que sucede cuando ambos móviles se acercan, expresando la formulación con signo negativo (-) como pueden ver.

Esta es la frecuencia del sonido percibido por el receptor cuando ambos móviles se acercan.

Análisis de los resultados

Para esta tercera condición del efecto Doppler, la cual nos indica que ambos móviles se encuentran en movimiento, es decir, tanto el receptor como el emisor del sonido, y de acuerdo a los cálculos realizados seguimos notando las mismas características de este particular fenómeno físico, el cual hace que la frecuencia percibida por el receptor, sea distinta a la emitida por el foco emisor del sonido (ambulancia).

Comprobando esta característica de igual manera cuando ambos móviles, se acercaban y alejaban uno del otro, por lo que este principio se cumple para las tres condiciones analizadas:

Primera condición: Receptor inmóvil, y foco emisor de sonido en movimiento.

Segunda condición: Receptor en movimiento, y emisor de sonido inmóvil.

Tercera condición: Receptor y emisor de sonido, ambos en movimiento.

Para estas tres condiciones, el receptor del sonido percibió una frecuencia distinta a la frecuencia emitida por el foco emisor del sonido, tanto al acercarse como al alejarse ambos. En la siguiente tabla observaran las relaciones de las frecuencias para esta tercera condición.

Pueden observar los anteriores artículos relacionados a las dos primeras condiciones analizadas en los siguientes enlaces:

1.- Efecto Doppler, receptor inmóvil.

2.- Efecto Doppler, receptor en movimiento y emisor inmóvil.

Hasta otra oportunidad mis queridos amigos.

Nota: Las imágenes fueron realizadas por el autor utilizando Power Point y Paint.

Referencias Bibliográficas recomendadas

[1] MOVIMIENTO ONDULATORIO. Link.

[2] Doppler Effect. Link.

Comments

[stemsocial]

Thanks for your contribution to the STEMsocial community. Feel free to join us on discord to get to know the rest of us!

Please consider delegating to the @stemsocial account (85% of the curation rewards are returned).

You may also include @stemsocial as a beneficiary of the rewards of this post to get a stronger support. 
 

[rbalzan79]

Thank you dear community for your important support. Regards

[alidickson]

That's a nice and educative exercise. Thanks alot for sharing.

[rbalzan79]

Thanks to you my friend for your visit and your words. Greetings.

[alidickson]

You are welcome Sir

[gwajnberg]

Nice draws! Very creative to explain the problem
!1UP

[rbalzan79]

Thank you for your support. Best regards.

[ramonycajal]

Su post ha sido valorado por @ramonycajal

[rbalzan79]

Gracias por el valioso apoyo a toda la comunidad de @Cervantes. Saludos.

[hivebuzz]

Congratulations @rbalzan79! You have completed the following achievement on the Hive blockchain and have been rewarded with new badge(s):

You got more than 2500 replies. Your next target is to reach 2750 replies.

_{You can view your badges on your board and compare yourself to others in the Ranking
If you no longer want to receive notifications, reply to this comment with the word STOP}

Check out the last post from @hivebuzz:

	Trick or Treat - Share your scariest story and win your Halloween badge
	Hive Power Up Day - November 1st 2022

Support the HiveBuzz project. Vote for our proposal!

[rbalzan79]

Thank you for the information provided. Best regards.

[hivebuzz]

You're welcome @rbalzan79! Have a nice day 😊👍

[curation-cartel]

	You have received a 1UP from @gwajnberg! The @oneup-cartel will soon upvote you with: @ccc-curator, @stem-curator, @neoxag-curator And they will bring !PIZZA 🍕.

^{Learn more about our delegation service to earn daily rewards. Join the Cartel on Discord.}

[rbalzan79]

Thank you for your support. Best regards.

[pizzabot]

🍕 PIZZA !

I gifted $PIZZA slices here:
@curation-cartel_(18/20) tipped @rbalzan79 (x1)

_{Send $PIZZA tips in Discord via tip.cc!}

[royalevidence]

Back then in school, one of the courses I always find it hard to understand is physics because of the calculation therein

[rbalzan79]

Hi, that usually happens, but, once you get to understand physics you realize how wonderful it is.

Thanks for your visit and comment. Regards.