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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

X

-axis has an equation given by

y = A\, e^{-\left(\dfrac{x}{a} + \dfrac{t}{T}\right)^2}

. Compute the wave speed.

Options

A $\dfrac{a}{T}$
B $\dfrac{T}{a}$
C $\dfrac{a^2}{T}$
D $aT$

Correct answer

A. $\dfrac{a}{T}$

Step-by-step solution

The equation of the given wave is

y = A e^{-\left(\dfrac{x}{a} + \dfrac{t}{T}\right)^2}

For a travelling wave, the phase is constant for a given point on the waveform:

\dfrac{x}{a} + \dfrac{t}{T} = \text{constant}

Differentiating with respect to time

t

:

\dfrac{1}{a}\dfrac{dx}{dt} + \dfrac{1}{T} = 0

\dfrac{dx}{dt} = -\dfrac{a}{T}

The wave speed is the magnitude of the wave velocity:

v = \left|\dfrac{dx}{dt}\right| = \dfrac{a}{T}

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