A pulse is propagating on a long stretched string along its length taken as positive x-axis. Shape of the string at t=0 is given by y=a2-x2 when |x|≤a=0 when |x|≥a. What is the general equation of pulse after some time 't', if it is travelling along positive x-direction with speed V ?

y ( x , t ) = a 2 − ( x - Vt ) 2 when | x - Vt | ≤ a = 0 when | x - Vt | ≥ a

y ( x , t ) = a 2 − ( x - Vt ) 2 when | x - Vt | ≤ a = 0 when | x - Vt | ≥ a

y ( x , t ) = a 2 + ( x + Vt ) 2 when | x + Vt | ≤ a = a when | x + Vt | ≥ a

y ( x , t ) = a 2 − ( x + Vt ) 2 when | x + Vt | ≤ a = x + Vt when | x + Vt | ≥ a

y ( x , t ) = a 2 − ( x - Vt ) 2 when | x - Vt | ≤ a = 0 when | x - Vt | ≥ a

y ( x , t ) = a 2 + ( x - Vt ) 2 when | x - Vt | ≤ a = a when | x + Vt | ≥ a

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A pulse is propagating on a long stretched string along its length taken as positive x-axis. Shape of the string at t=0 is given by $y = \sqrt{a^{2} - x^{2}}$ when $| x | \leq a = 0$ when $| x | \geq a$ . What is the general equation of pulse after some time 't', if it is travelling along positive x-direction with speed V ?

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$y (x, t) = \sqrt{a^{2} + (x + Vt)^{2}}$ when $| x + Vt | \leq a = a$ when $| x + Vt | \geq a$

$y (x, t) = \sqrt{a^{2} - (x + Vt)^{2}}$ when $| x + Vt | \leq a = x + Vt$ when $| x + Vt | \geq a$

$y (x, t) = \sqrt{a^{2} - (x - Vt)^{2}}$ when $| x - Vt | \leq a = 0$ when $| x - Vt | \geq a$

$y (x, t) = \sqrt{a^{2} + (x - Vt)^{2}}$ when $| x - Vt | \leq a = a$ when $| x + Vt | \geq a$

answer is C.

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Replace 'x' by x - vt

i.e., $y = \sqrt{a^{2} - (x - vt)^{2}}$

where $| x - vt | \leq a = 0$ when $| x - vt | \geq a$

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