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Calculation of the duration (time) of a sound wave reflection and its wavelength / (Eng-Esp) by rbalzan79

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Calculation of the duration (time) of a sound wave reflection and its wavelength / (Eng-Esp)
<center>![Portada.jpg](https://images.hive.blog/DQmXRzv7Pmj7un9kqQbNNC4itWhexqBCdhjciDAmVfbvXUF/Portada.jpg)</center>


<div class="text-justify">Greetings again my dear friends as always hoping that you are all very well, we continue checking how the phenomenon of sound when propagating through certain material or elastic medium, important intrinsic phenomena originate to such propagation, this we began to analyze in the previous <a href="https://hive.blog/hive-196387/@rbalzan79/calculation-of-the-distance-of-a-sound-reflection-and-its-frequency-of-emission-eng-esp">article</a>  through the phenomenon of sound wave reflection, which is originated by the fact that the waves in their journey from one space-time to another, come across different obstacles that cause them to change direction and sense.
<p>

In order to further investigate the intrinsic phenomenon of sound reflection, we will analyze another example by means of an exercise such as the one you can see below:

<b>Exercise</b>

A person who is in a rocky area decides to try to generate a rebound of his voice in front of a huge rock, that is, the reflection of the sound waves produced by the vibration of his vocal cords, this person has in his hands a portable instrument that allows him to measure the frequency of the sound of his voice, which is 180 Hz, the distance at which he is from the huge rock is 14 m, in relation to all the above, answer the following questions:

<b>a.- What is the wavelength of the emitted sound?</b>

<b>b.- What is the time taken by the waves to reflect and return to the source of the sound, and in relation to this time, the auditory system of that person is able to perceive the echo phenomenon?</b>

<b>Solution</b>

<b>Data:</b>

ʎ = ? (Wavelength).
fo =  180 Hz (Sound frequency of the emitting source). 
dt = 28 m (Total distance of sound reflection).
do = 14 m (Distance between the person and the huge rock).
Vm = 340 m/s (Velocity of the sound propagation medium, in this case the air)
t = ? (Total sound reflection time).

a.- We start by solving our first unknown related to the calculation of the wavelength of the sound emitted by the person in front of the rock, and to do so, we implement the following equation.

<center>![Fórmula_1.jpg](https://images.hive.blog/DQmcntBVjFbX3oX2Y2ubwh3rDYSqF12Tyqr6Ph1z3soKm42/F%C3%B3rmula_1.jpg)</center>

From the above formula we have two variables, so we proceed to clear the requested variable, i.e. the wavelength (ʎ):

<center>![Fórmula_2_Y cálculo de la longitud de onda.jpg](https://images.hive.blog/DQmQVnU35E1oKEAAHFNNYyYHK2SLdqB5AkQ5iLsjg3NvbLP/F%C3%B3rmula_2_Y%20c%C3%A1lculo%20de%20la%20longitud%20de%20onda.jpg)</center>

After the calculation of the wavelength of the emitted sound, we proceed to solve our second question.

b.- To solve for this unknown, we use the following formula for the distance and then clear time.

<center>![Fórmula_3.jpg](https://images.hive.blog/DQmV9LmDWXLQ3hQhjPxz3B3QNGM4HDmFf7KexobqtDFLsUa/F%C3%B3rmula_3.jpg)</center>

<center>![Fórmula_4.jpg](https://images.hive.blog/DQmcVi3s57jEf5L3fruyuQbAccfzCS4b5RqtFJji96y33Lk/F%C3%B3rmula_4.jpg)</center>

This is the value of the time taken by the sound waves to travel the total distance (dt) of 28 meters, therefore, the distance of 14 m is traveled by the sound waves in 0.041 s.

In relation to whether the person captures the generation of the echo phenomenon, we can express that the auditory system of the human being has the ability to distinguish two consecutive sounds, provided that between these sounds there is at least a difference of one tenth of a second (0.1 s), therefore, if we take this relationship and, knowing that the standard speed of sound in the air is 340 m/s, any person under these conditions would have to be at a minimum distance of 17 meters, where the total distance was 34 m, and thus to hear the echo of his voice.

Therefore, in relation to the above, it is determined that the person who was in front of the huge rock could not perceive the echo phenomenon, because he was not at the minimum distance to be able to capture the echo phenomenon, since he was 14 meters away, for a total distance of 28 meters, and a time of 0.082 seconds, so the conditions mentioned above are not met and the echo has not been originated.

In such a case, the person managed to perceive another phenomenon developed during the reflection of sound waves such as reverberation, the echo is an acoustic phenomenon that originates when the receiver receives the emitted wave as the reflected wave, and detects them as two different sounds, as for the phenomenon of reverberation originates a superposition of the emitted wave with respect to the reflected sound wave.

<h1>Analysis of results</h1>

Sound never ceases to amaze us by its wonderful intrinsic phenomena, such as reflection, and this in turn, has other even more intrinsic phenomena such as echo and reverberation, and these phenomena, related to the distance of the emitting focus and the reflecting surface of the sound waves, and of course, the material or elastic medium through which any acoustic signal is propagated.

In general, our voice propagates through the material medium such as air, where the propagation speed is 340 m/s, and in relation to the reflection of sound waves to be an echo for the human ear, there must be a time differential of at least 0.1 second between two consecutive sounds, and in the air, the minimum distance must be 17 m, between the emitter and the receiving surface of the sound waves.

In the present case, the person in our example did not manage to capture the phenomenon of echo, but that of reverberation, according to the conditions given and described for the generation of an echo, through the reflection of certain sound waves, produced by our voice or any other source of natural or artificial origin, later we will continue with our purpose of knowing a little more about the wonderful phenomenon of sound.

Until another opportunity my dear friends.</div>

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

<h1>Recommended Bibliographic References</h1>

[1] MOVIMIENTO ONDULATORIO. <a href="https://www.uv.mx/personal/aherrera/files/2014/05/D1.-Movimiento-ondulatorio.pdf">Link.</a>

[2] Reflection of underwater sound from surface waves. <a href="https://courses.physics.ucsd.edu/2009/Spring/physics2c/documents/2.3DopplerShift.notes.pdf">Link.</a>

[3] REFLEXIÓN Y REFRACCIÓN DEL SONIDO. <a href="http://www.alsarica.cl/ckfinder/userfiles/files/material/surrejola/Fisica/Fisica%201%20Medio/Gu%C3%ADa%20de%20Ondas%20y%20Sonido%20-%201%C2%B0%20Medio%20-%202017.pdf">Link.</a>

[4] SPEED OF SOUND. <a href="https://www.cerritos.edu/cmera/Physics101/Lab/Sound/Speed_of_Sound.pdf">Link.</a>

[5] Echo-based measurement of the speed of sound. <a href="https://arxiv.org/ftp/arxiv/papers/1102/1102.2664.pdf">Link.</a>

[6] Propiedades de las ondas sonoras . <a href="https://www.colegiostmf.cl/wp-content/uploads/2020/05/I-Medio-Fisica-guia-4.pdf">Link.</a></div>

<center><h1>Spanish version</h1></center>

<center>![Portada_Spanish.jpg](https://images.hive.blog/DQma6q3hW9pkD5N4fmCJQBfDGML5MbB5Bqr86zhMawXUc1g/Portada_Spanish.jpg)</center>

<div class="text-justify">Saludos de nuevo mis queridos amigos como siempre esperando que se encuentren todos muy bien, seguimos comprobando como el fenómeno del sonido al propagarse por determinado medio material o elástico, se originan importantes fenómenos intrínsecos a dicha propagación, esto lo comenzamos a analizar en el anterior <a href="https://pixabay.com/es/photos/atardecer-sonido-nubes-paisaje-2416859/">artículo</a>  mediante el fenómeno de la reflexión de las ondas sonoras, el cual se origina por el hecho de que las ondas en su recorrido de un espacio-tiempo a otro, llegan a encontrarse con distintos obstáculos que hacen que las mismas cambien de dirección y sentido.
<p>

Con la finalidad de seguir indagando sobre el intrínseco fenómeno de la reflexión del sonido, analizaremos otro ejemplo, por medio, de un ejercicio como el que pueden observar a continuación:

<b>Ejercicio</b>

Una persona que se encuentra en una área rocosa decide tratar de generar un rebote de su voz frente a una enorme roca, es decir, la reflexión de las ondas sonoras producidas por la vibración de sus cuerdas vocales, esta persona posee en sus manos un instrumento portátil que le permite medir la frecuencia del sonido de su voz, la cual es de 180 Hz, la distancia a la que se encuentra de la enorme roca es de 14 m, en relación a todo lo antes expuesto, responder a las siguientes interrogantes:

<b>a.-¿Cuál es la longitud de onda del sonido emitido?</b>

<b>b.-¿Cuál es el tiempo empleado por las ondas en reflejarse y volver hasta el foco emisor del sonido, y en relación a este tiempo, el sistema auditivo de dicha persona logra percibir el fenómeno del eco?</b>

<b>Solución</b>

<b>Datos:</b>

ʎ = ? (Longitud de onda).
fo =  180 Hz (Frecuencia del sonido del foco emisor). 
dt = 28 m (Distancia total de la reflexión del sonido).
do = 14 m (Distancia entre la persona y la enorme roca).
Vm = 340 m/s (Velocidad del medio de propagación del sonido (El aire en este caso)
t = ? (Tiempo total de la reflexión del sonido).

a.- Comenzamos resolviendo nuestra primera incógnita relacionada al cálculo de la longitud de onda del sonido emitido por la persona que se encuentra frente a la roca, y para ello, implementamos la siguiente ecuación.

<center>![Fórmula_1.jpg](https://images.hive.blog/DQmcntBVjFbX3oX2Y2ubwh3rDYSqF12Tyqr6Ph1z3soKm42/F%C3%B3rmula_1.jpg)</center>

De la anterior fórmula poseemos dos variables, por lo que procedemos a despejar la variable solicitada, es decir, la longitud de onda (ʎ):

<center>![Fórmula_2_Y cálculo de la longitud de onda.jpg](https://images.hive.blog/DQmQVnU35E1oKEAAHFNNYyYHK2SLdqB5AkQ5iLsjg3NvbLP/F%C3%B3rmula_2_Y%20c%C3%A1lculo%20de%20la%20longitud%20de%20onda.jpg)</center>

Luego del cálculo de la longitud de onda del sonido emitido, procedemos a resolver nuestra segunda incógnita.

b.- Para pasar a resolver esta incógnita utilizamos la siguiente fórmula de la distancia para luego despejar el tiempo.

<center>![Fórmula_3.jpg](https://images.hive.blog/DQmV9LmDWXLQ3hQhjPxz3B3QNGM4HDmFf7KexobqtDFLsUa/F%C3%B3rmula_3.jpg)</center>

<center>![Fórmula_4.jpg](https://images.hive.blog/DQmcVi3s57jEf5L3fruyuQbAccfzCS4b5RqtFJji96y33Lk/F%C3%B3rmula_4.jpg)</center>

Este es el valor del tiempo implementado por las ondas sonoras para recorrer la distancia total (dt) de los 28 metros, por lo tanto, la distancia de los 14 m, las ondas sonoras la recorren en 0,041 s.

En relación a que, si la persona capta la generación del fenómeno del eco, podemos expresar que el sistema auditivo del ser humano posee la capacidad de distinguir dos sonidos consecutivos, siempre y cuando, entre estos sonidos existe como mínimo una diferencia de una décima de segundo (0,1 s), por lo tanto, si tomamos esta relación y, sabiendo que la velocidad estándar del sonido en el aire es de 340 m/s, cualquier persona bajo estas condiciones tendría que estar a una distancia mínima de 17 metros, donde el recorrido total fuese 34 m, y de esta manera poder escuchar el eco de su voz.

Entonces, en relación a lo antes expresado, se determina que la persona que se encontraba frente a la enorme roca no pudo percibir el fenómeno del eco, debido a que no se encontraba a la distancia mínima para poder captar dicho fenómeno del eco, ya que estuvo a 14 metros, para un recorrido total de 28 metros, y un tiempo de 0,082 segundos, por lo que no se cumple las condiciones antes señaladas y, el eco no se ha originado.

En tal caso, la persona logro percibir otro fenómeno desarrollado durante la reflexión de las ondas sonoras como es el de la reverberación, el eco es un fenómeno acústico que se origina cuando al receptor llega la onda emitida como como la onda reflejada, y las detecta como dos sonidos diferentes, en cuanto al fenómeno de la reverberación se origina una superposición de la onda emitida con respecto a la onda sonora reflejada.

<h1>Análisis de los resultados</h1>

El sonido no deja de sorprendernos por sus maravillosos fenómenos intrínsecos, como el de su reflexión, y este a la vez, posee otros fenómenos aún más intrínsecos como el del eco y reverberación, y dichos fenómenos, relacionados con la distancia del foco emisor y la superficie reflectora de las ondas sonoras, y por supuesto, el medio material o elástico por donde se propagan cualquier señal acústica.

Por lo general, nuestra voz se propaga por el medio material como el aire, en donde, la velocidad de propagación es de 340 m/s, y en relación a la reflexión de las ondas sonoras para que sea un eco para el oído humano, debe existir un diferencial de tiempo de 0,1 segundo como mínimo entre dos sonidos consecutivos, y en el aire, la distancia mínima debe ser de 17 m, entre el emisor y la superficie receptora de las ondas sonoras.

Para el presente caso la persona de nuestro ejemplo no logro captar el fenómeno del eco, sino, el de la reverberación, de acuerdo a las condiciones dadas y las descritas para la generación de un eco, por medio de la reflexión de determinadas ondas sonoras, producidas por nuestra voz o cualquier otra fuente de origen natural como artificial, más adelante seguiremos con nuestro propósito planteado de conocer un poco más sobre el maravilloso fenómeno del sonido.

Hasta otra oportunidad mis queridos amigos.</div>

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

<h1>Referencias Bibliográficas recomendadas</h1>

[1] MOVIMIENTO ONDULATORIO. <a href="https://www.uv.mx/personal/aherrera/files/2014/05/D1.-Movimiento-ondulatorio.pdf">Link.</a>

[2] Reflection of underwater sound from surface waves. <a href="https://courses.physics.ucsd.edu/2009/Spring/physics2c/documents/2.3DopplerShift.notes.pdf">Link.</a>

[3] REFLEXIÓN Y REFRACCIÓN DEL SONIDO. <a href="http://www.alsarica.cl/ckfinder/userfiles/files/material/surrejola/Fisica/Fisica%201%20Medio/Gu%C3%ADa%20de%20Ondas%20y%20Sonido%20-%201%C2%B0%20Medio%20-%202017.pdf">Link.</a>

[4] SPEED OF SOUND. <a href="https://www.cerritos.edu/cmera/Physics101/Lab/Sound/Speed_of_Sound.pdf">Link.</a>

[5] Echo-based measurement of the speed of sound. <a href="https://arxiv.org/ftp/arxiv/papers/1102/1102.2664.pdf">Link.</a>

[6] Propiedades de las ondas sonoras . <a href="https://www.colegiostmf.cl/wp-content/uploads/2020/05/I-Medio-Fisica-guia-4.pdf">Link.</a></div>
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@rbalzan79 ·
Gracias por el valioso apoyo a la familia de @Cervantes. Saludos.
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@royalevidence ·
This article made me to remember my secondary school days when I was a lover of physics 
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vote details (1)
@rbalzan79 ·
Hi, thanks for your comment, and physics always gives us the pleasure of being able to fall in love with it. Greetings.
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@stemsocial ·
re-rbalzan79-calculation-of-the-duration-time-of-a-sound-wave-reflection-and-its-wavelength-eng-esp-20221126t172255604z
<div class='text-justify'> <div class='pull-left'>
 <img src='https://stem.openhive.network/images/stemsocialsupport7.png'> </div>

Thanks for your contribution to the <a href='/trending/hive-196387'>STEMsocial community</a>. Feel free to join us on <a href='https://discord.gg/9c7pKVD'>discord</a> 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.&nbsp;<br />&nbsp;<br />
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@rbalzan79 ·
Thank you dear @stemsocial community for such valuable support. Regards.
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