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? Options: A . &nbspa B . &nbsp-a C . &nbsp1a D . &nbsp2a

Answer: Option B : B y = A e − ( x a + t T ) 2 at t=T the pulse would be y = A e − ( x a + 1 ) 2 d y d x = − 2 A a ( x a + 1 ) e − ( x a + 1 ) 2 d y d x = 0 ⇒ x a + 1 = 0 x = − a

The equation of a wave travelling on a string stretched along the X-axis is give

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?

Options:

A . a

B . -a

C . 1a

D . 2a

Answer: Option B
:
B

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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