Answer
342k+ views
Hint: A type of wave in which all the particles perform simple harmonic motion about their mean position. The equation of plane progressive waves is determined by using the concept of simple harmonic motion. All the particles have the same amplitude in the plane progresive wave.
Complete answer:
A plane progressive harmonic wave is a wave which travels in given directions without change of its form and every particle of medium performs simple harmonic motion about their mean position with equal amplitude and time period.
When we consider a particle at point $P$ at $x$ distance from origin $O $. The particle performs simple harmonic motion with equal amplitude and time period. The disturbance at $O$ travels and reaches point $P$ after some time. Hence the displacement of particle from equilibrium position at time $t$ is given by
$y=asin(\omega t-\varphi )$
where, $a$=amplitude, $\omega =$Angular Frequency and $\varphi =$phase difference
Phase difference depends on the path difference OP
$\varphi =\dfrac{2\pi x}{\lambda }$
where, x$=$path difference and $\lambda =$ wavelength.
$y=a\sin (\omega t-\dfrac{2\pi x}{\lambda })$
$\therefore y=a\sin (\omega t-kx)$..............$(\because k=\dfrac{\text{2}\pi }{\lambda })$
Where, $k$ is Angular wave number.
Characteristics of a Plane Progressive harmonic wave:
-When there is a disturbance in any wave then all the particles of the medium perform simple harmonic motion.
-All the particles have same amplitude
-All the particles vibrate with same frequency
-Energy is transmitted through the medium
Note:When the wave disturbance travel in positive x-axis then the equation is
$y=a\sin (\omega t-kx)$. When the wave travels in the negative x-axis then the equation is $y=a\sin (\omega t+kx)$. Somewhere the equation will be $y=a\sin (\omega t-kx+\partial)$ where the $\partial $ is the initial phase difference. In the above derivation we take the initial phase difference to be zero.
Complete answer:
A plane progressive harmonic wave is a wave which travels in given directions without change of its form and every particle of medium performs simple harmonic motion about their mean position with equal amplitude and time period.
![seo images](https://www.vedantu.com/question-sets/a41df28d-2e3a-474e-be77-fe7968d8f6075523751267654413748.png)
When we consider a particle at point $P$ at $x$ distance from origin $O $. The particle performs simple harmonic motion with equal amplitude and time period. The disturbance at $O$ travels and reaches point $P$ after some time. Hence the displacement of particle from equilibrium position at time $t$ is given by
$y=asin(\omega t-\varphi )$
where, $a$=amplitude, $\omega =$Angular Frequency and $\varphi =$phase difference
Phase difference depends on the path difference OP
$\varphi =\dfrac{2\pi x}{\lambda }$
where, x$=$path difference and $\lambda =$ wavelength.
$y=a\sin (\omega t-\dfrac{2\pi x}{\lambda })$
$\therefore y=a\sin (\omega t-kx)$..............$(\because k=\dfrac{\text{2}\pi }{\lambda })$
Where, $k$ is Angular wave number.
Characteristics of a Plane Progressive harmonic wave:
-When there is a disturbance in any wave then all the particles of the medium perform simple harmonic motion.
-All the particles have same amplitude
-All the particles vibrate with same frequency
-Energy is transmitted through the medium
Note:When the wave disturbance travel in positive x-axis then the equation is
$y=a\sin (\omega t-kx)$. When the wave travels in the negative x-axis then the equation is $y=a\sin (\omega t+kx)$. Somewhere the equation will be $y=a\sin (\omega t-kx+\partial)$ where the $\partial $ is the initial phase difference. In the above derivation we take the initial phase difference to be zero.
Recently Updated Pages
In a flask the weight ratio of CH4g and SO2g at 298 class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In a flask colourless N2O4 is in equilibrium with brown class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In a first order reaction the concentration of the class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In a first order reaction the concentration of the class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In a fermentation tank molasses solution is mixed with class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In a face centred cubic unit cell what is the volume class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Which of the following is the most stable ecosystem class 12 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which of the following is the most stable ecosystem class 12 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write an application to the principal requesting five class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The term vaccine was introduced by A Jenner B Koch class 12 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)