Equation of a Travelling wave pulse wave Function is given by - - sin - - - - - - Then find the expressions for particle velocity-

Equation is 𝐲 = sin ( 𝐤 #10;𝐗 ω 𝐭 ) #10; #10; y = A sin( 2 π #10;λ x 2 π v λ #10; t ) = A sin( 2 πλ #10; x 2 π T t ) ...

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Standard XII

Physics

Reflection from a Fixed End

Equation of a...

Question

Equation of a Travelling wave pulse (wave Function) is given by $y = sin (k x - ω t)$ .
Then find the expressions for particle velocity.

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Solution

Equation is $y = sin (k X - ω t)$

$y = A sin (\frac{2 π}{λ} x - \frac{2 π v}{λ} t) = A sin (\frac{2 π}{λ} x - \frac{2 π}{T} t)$

Angular velocity, $ω = \frac{2 π}{T} = 2 π (\begin{matrix} number of periods per unit time \end{matrix})$

Wave number, $k = \frac{2 π}{λ} = 2 π (\begin{matrix} number of wavelengths per unit length \end{matrix}$

$\frac{ω}{k} = \frac{2 π / T}{2 π / λ} = \frac{λ}{T} = v$

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Equation of a Travelling wave pulse (wave Function) is given by y=sin(kx−ωt). Then find the expressions for particle velocity.

Equation is y=sin(kX−ωt) y=Asin(2πλx−2πvλt)=Asin(2πλx−2πTt) Angular velocity, ω=2πT=2π( number of periods per unit time ) Wave number,k=2πλ=2π( number of wavelengths per unit length ωk=2π/T2π/λ=λT=v

Equation of a Travelling wave pulse (wave Function) is given by $y = sin (k x - ω t)$ .
Then find the expressions for particle velocity.