Question

Which of the following functions represents a travelling wave? Here, a,b,c are constants.
I. y = a cos bx sin ct II. y = asin (bx + ct)
III. y = a sin (bx - ct)+b sin (bx – ct) IV. y = a sin (bx - ct)

• A. Both I and IV
• B. Both I and II
• C. Both II and IV
• D. Both II and III

Answer 1

The correct option is C Both II and IV

The equation should satisfy $\frac{\partial y}{\partial t^2}=v^2\frac{\partial y}{\partial x^2}$
This will be satisfied by II and IV Besides satisfying the equation y should be finite everywhere (i.e. for all values of x) all the time (i.e. for all values of t)