Q. Given the wavefunction (in SI units) for a wave to be $\psi_{(x,\ t)} = 10^{3}\sin{\pi(3 \times 10^{6}\ x - 9 \times 10^{14}\ t)}$ The speed of the wave is
A) $9 \times 10^{14}\ ms^{- 1}$
B) $3 \times 10^{8}\ ms^{- 1}$
C) $3 \times 10^{6}\ ms^{- 1}$
D) $3 \times 10^{7}\ ms^{- 1}$
Explanation
(b) $\psi_{(x,\ t)} = 10^{3}\sin{\pi\left( 3 \times 10^{6}\ x - 9 \times 10^{14}\ t \right)}$
$= 10^{3}\sin{3 \times 10^{6}\ \pi(x - 3 \times 10^{8}\ t)}$
Comparing it with the relation
$\psi_{(x,\ t)} = a\sin\frac{2\pi}{\lambda}(x - ct)$; We note that
$c = 3 \times 10^{8}\ ms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.