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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 stretched string carries a wave in the positive x -direction with...

A stretched string carries a wave in the positive

x

-direction with a wave speed of

v

. The displacement of the particle at

x = 0

is described by

f(t) = A \sin(t/T)

. Determine the wave equation.

Options

A $f(x, t) = A \sin \left(\dfrac{t}{T} + \dfrac{x}{vT}\right)$
B $f(x, t) = A \sin \left(\dfrac{t}{T} + \dfrac{x}{v}\right)$
C $f(x, t) = A \sin \left(\dfrac{t}{T} - \dfrac{x}{v}\right)$
D $f(x, t) = A \sin \left(\dfrac{t}{T} - \dfrac{x}{vT}\right)$

Correct answer

D. $f(x, t) = A \sin \left(\dfrac{t}{T} - \dfrac{x}{vT}\right)$

Step-by-step solution

For a wave traveling in the positive

x

-direction with speed

v

, the displacement

f(x, t)

at any position

x

and time

t

is given by the displacement at

x = 0

at an earlier time

t - \dfrac{x}{v}

.

Given the displacement at

x = 0

is

f(t) = A \sin \left(\dfrac{t}{T}\right).<br><br>Substituting

t

with

t -

\dfrac{x}{v} gives the wave equation:<br><br>

f(x, t) = A \sin \left(\dfrac{t - \dfrac{x}{v}}{T}\right)

<br><br>

f(x, t) = A \sin \left(\dfrac{t}{T} - \dfrac{x}{vT}\right)

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