time in Sine Wave equation
In the context that you described, $t$ is a variable indicating time. That is, the wave will take on a value of $y(t)$ at the time instant $t$. If this is measured in seconds, then $\omega$ specifies the number of radians that the wave passes through in one second. And, as you noted, if the wave has a frequency of $\frac{100}{15}\ \text{Hz}$, then it will pass through 100 periods in 15 seconds.