A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by, $y ( x , t ) = 0.5 \sin \left( \frac { 5 \pi } { 4 } x \right) \cos ( 200 \pi t )$. What is the speed of the travelling wave moving in the positive $x$ direction? ($x$ and $t$ are in meter and second, respectively) (1) $120 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ (2) $90 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ (3) $160 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ (4) $180 \mathrm {~m} \mathrm {~s} ^ { - 1 }$
A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by, $y ( x , t ) = 0.5 \sin \left( \frac { 5 \pi } { 4 } x \right) \cos ( 200 \pi t )$. What is the speed of the travelling wave moving in the positive $x$ direction? ($x$ and $t$ are in meter and second, respectively)\\
(1) $120 \mathrm {~m} \mathrm {~s} ^ { - 1 }$\\
(2) $90 \mathrm {~m} \mathrm {~s} ^ { - 1 }$\\
(3) $160 \mathrm {~m} \mathrm {~s} ^ { - 1 }$\\
(4) $180 \mathrm {~m} \mathrm {~s} ^ { - 1 }$