JEE Main · 2011 · 10 Apr 2011 · Offline · Waves & Sound

The transverse displacement

y (x, t)

of a wave on a string is given by

y (x, t) = e^{- (a x^{2} + b t^{2} + 2 ab x t)}

. This represents a

Answer: (A)

Solution

The exponent is a perfect square,

a x^{2} + b t^{2} + 2 ab x t = (a x + b t)^{2}

, so

y (x, t) = e^{- (a x + b t)^{2}}

. The displacement depends on

x

and

t

only through the combination

a x + b t

, which is the signature of a travelling wave of the form

f (x + v t)

moving in the negative

x

direction. Writing the group as

a (x + b / a t)

identifies the speed as

v = b / a

, so this is a wave moving in the

- x

direction with speed

b / a

JEE Main · 2011 · 10 Apr 2011 · Offline · Single correct option