The equation of a wave travelling on a string stretched along the X-axis is given by y - A e -x- a - t - T 2 Where is the maximum of the pulse located at t - T -A- 2 aB- aC- -aD- 1 - a

The correct option is C a y=A e^ (x/a+t/T)^2 at t=T the pulse would be y=A e^ (x/a+1)^2 dy/dx= 2A/a(x/a+1) e^ (x/a+1)^2 dy/dx=0 ⇒ x/a+1=0 x= a ...

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Standard XII

Physics

Wave Equation

The equation ...

Question

The equation of a wave travelling on a string stretched along the X-axis is given by $y = A e^{- {(\frac{x}{a} + \frac{t}{T})}^{2}}$

Where is the maximum of the pulse located at t = T?

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-a

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1/a

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Solution

The correct option is B
-a

$y = A e^{- {(\frac{x}{a} + \frac{t}{T})}^{2}}$

at t=T the pulse would be

$y = A e^{- {(\frac{x}{a} + 1)}^{2}}$

$\frac{d y}{d x} = \frac{- 2 A}{a} (\frac{x}{a} + 1) e^{- {(\frac{x}{a} + 1)}^{2}}$

$\frac{d y}{d x} = 0 \Rightarrow \frac{x}{a} + 1 = 0$

$x = - a$

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The equation of a wave travelling on a string stretched along the X-axis is given by y=A e−(xa+tT)2 Where is the maximum of the pulse located at t = T?

The correct option is B -a y=A e−(xa+tT)2 at t=T the pulse would be y=A e−(xa+1)2 dydx=−2Aa(xa+1) e−(xa+1)2 dydx=0 ⇒ xa+1=0 x=−a

The equation of a wave travelling on a string stretched along the X-axis is given by $y = A e^{- {(\frac{x}{a} + \frac{t}{T})}^{2}}$

Where is the maximum of the pulse located at t = T?

The correct option is B
-a

$y = A e^{- {(\frac{x}{a} + \frac{t}{T})}^{2}}$

at t=T the pulse would be

$y = A e^{- {(\frac{x}{a} + 1)}^{2}}$

$\frac{d y}{d x} = \frac{- 2 A}{a} (\frac{x}{a} + 1) e^{- {(\frac{x}{a} + 1)}^{2}}$

$\frac{d y}{d x} = 0 \Rightarrow \frac{x}{a} + 1 = 0$

$x = - a$