A travelling pulse is f(x,t) = A exp{[2abxt − a²x² − b²t²]/c²}, where A, a, b and c are positive constants. Find the pulse speed.
Physics · Wave Motion
JEE Mains Advanced

Question

A travelling pulse is f(x,t) = A exp{[2abxt − a²x² − b²t²]/c²}, where A, a, b and c are positive constants. Find the pulse speed.

G1 Physics · Accepted Answer

Step 1: 2abxt − a²x² − b²t² = −(ax − bt)². Step 2: The pulse maximum satisfies ax − bt = 0, so x = (b/a)t. Hence pulse speed = b/a. Final: A.