Answer:
Shortest time = 58.18 × 10^(-6) s
Explanation:
We are given;
s(x,t) = 5.00 nm cos((60.00 m^(−1)x) − (18.00 X 10³ s^(−1)t))
Let us set x = 0 as origin.
Now, for us to find the time difference, we need to solve 2 equations which are;
s(x,t) = 5.00 nm cos((60.00 m^(−1)x) − (18.00 X 10³ s^(−1)t1))
And
s(x,t) = 5.00 nm cos((60.00 m^(−1)x) − (18.00 X 10³ s^(−1)t2))
Now, since the wave starts from maxima at time at t = 0, the required time would be the difference (t2 - t1)
Thus, the solutions are;
t1 = (1/(18 × 10³)) cos^(-1) (2.5/5)
And
t2 = (1/(18 × 10³)) cos^(-1) (-2.5/5)
Angle of the cos function is in radians, thus;
t1 = 58.18 × 10^(-6) s
t2 = 116.36 × 10^(-6) s
So,
Required time = t2 - t1 = (116.36 × 10^(-6) s) - (58.18 × 10^(-6) s) = 58.18 × 10^(-6) s
