Answer: 3 radians/meter.
Explanation:
The general sinusoidal function will be something like:
y = A*sin(k*x - ω*t) + C
Where:
A is the amplitude.
k is the wave number.
x is the spatial variable
ω is the angular frequency
t is the time variable.
C is the mid-value.
The rule that we can use to solve this problem, is that the argument of the sin( ) function must be in radians (or in degrees)
Then if x is in meters, the wave-number must be in radians/meters, so when these numbers multiply the "meters" part is canceled.
Then for the case of the function:
y(x,t) = 0.1 sin(3x + 10t)
Where x is in meters, the units of the wave number (the 3) must be in radians/meters. Then the angular wave number is 3 radians/meter.
An object in motion tends to stay in motion an oject at rest stays at rest.
Given the index of refraction, n and speed of light in the vacuum, c, we can solve for the speed of light in the transparent substance by the equation below.
n = c / v
where v is our unknown.
Substituting the known values,
1.7 = (3 x 10^8 m/s) / v
The value of v is equal to 1.76 x 10^8 m/s.
