A wave is described by y(x, t) = 0.1 sin(3x + 10t), where x is in meters, y is in centimeters and t is in seconds. The angular wave number is:

Angular wave number is measured in rad/s. the angular wave number in the given equation is 10 rad/s.

Angular wave number:

It is the number of wavelengths per unit distance. It is also known as angular frequency.  It is measured in rad/s.

For given equation,

Angular wave number  is the parameter which is multiplied by time (t). So, it is the number 10,  this will be measured in rad/s.  

Therefore, the angular wave number in the given equation is 10 rad/s.

To know more about angular wave number, refer to the link:

link

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.