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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Wave Motion and Waves on a String

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Wave Motion and Waves on a String

A wave travelling on a string stretched along the X -axis has an...

A wave travelling on a string stretched along the XX-axis has an equation given by y=A e−(xa+tT)2y = A\, e^{-\left(\dfrac{x}{a} + \dfrac{t}{T}\right)^2}. Locate the maximum of the pulse at t=Tt = T and at t=2Tt = 2T respectively.

Options

  1. Ax=−ax = -a and x=−2ax = -2a
  2. Bx=ax = a and x=2ax = 2a
  3. Cx=−ax = -a and x=ax = a
  4. Dx=2ax = 2a and x=ax = a

Correct answer

A. x=−ax = -a and x=−2ax = -2a

Step-by-step solution

The given equation of the wave is y=Ae−(xa+tT)2y = A e^{-\left(\dfrac{x}{a} + \dfrac{t}{T}\right)^2}.

The maximum value of the pulse occurs when the exponent is zero, since the function e−z2e^{-z^2} is maximum at z=0z = 0.

xa+tT=0\dfrac{x}{a} + \dfrac{t}{T} = 0

x=−aTtx = -\dfrac{a}{T} t

At t=Tt = T, the position of the maximum is:

x=−aT(T)=−ax = -\dfrac{a}{T} (T) = -a

At t=2Tt = 2T, the position of the maximum is:

x=−aT(2T)=−2ax = -\dfrac{a}{T} (2T) = -2a
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