Time-varying waveform
Consider the function $\sin(2\pi f t)$. When $2\pi f t$ goes from $0$ to $2\pi$ you get oscillation of the sine wave, $2\pi$ to $4\pi$, another, and so on. So every time the argument changes by $2\pi$ you get one oscillation.

Now lets plot $2\pi f(t) t$ where $f(t) = 10 + 10 \sin(2 \pi t)$. (I've modified it a bit to show the effect more):



As $t$ increases, this value changes faster and faster, meaning $\sin(2\pi f(t) t)$ will have higher and higher frequency.

Another way of thinking about it - the frequency is the derivative of $f(t) t$. For the example this is $20 \pi (\sin(2 \pi t)+2 \pi \mathbf{t} \cos(2 \pi t)+1)$. Note the $t$ multiplier in there - $t$ increases thus the frequency increases.

So what you really want is 
$\tfrac{d}{dt} f(t) t = 40 + 10 \sin(t)$ which gives $f(t) t = 40t - 10\cos(t) + c$ and for your example try $ \sin(2\pi(40t - 10 \cos(t)))$