A wave pulse travels on a string towards the positive X -axis with a speed v . At t = 0 , the shape of the string is given by g(x) = A (x/a) , where A and a are constants. Write the equation of the wave for a general

Correct answer: A. f(x, t) = A ((x - vt)/(a)) For a wave traveling in the positive x -direction with speed v , the wave equation f(x, t) must be a function of (x - vt) . Given the shape of the wave at t = 0 is g(x) = A ((x)/(a)). Replacing x with (x - vt) in the expression for g(x) gives the equation of the wave at any general time t . Thus, f(x, t) = g(x - vt) = A ((x - vt)/(a)) .

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 pulse travels on a string towards the positive X -axis with...

A wave pulse travels on a string towards the positive

X

-axis with a speed

v

. At

t = 0

, the shape of the string is given by

g(x) = A \sin(x/a)

, where

A

and

a

are constants. Write the equation of the wave for a general time

t

Options

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

Correct answer

A. $f(x, t) = A \sin \left(\dfrac{x - vt}{a}\right)$

Step-by-step solution

For a wave traveling in the positive

x

-direction with speed

v

, the wave equation

f(x, t)

must be a function of

(x - vt)

.

Given the shape of the wave at

t = 0

g(x) = A \sin \left(\dfrac{x}{a}\right).<br><br>Replacing

with

(x - vt)

in the expression for

g(x)

gives the equation of the wave at any general time

.<br><br>Thus,

f(x, t) = g(x - vt) = A \sin \left(\dfrac{x - vt}{a}\right)

.

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