Adding sine wave with different amplitude and different frequency How to express the following equation into a sine wave equation ? 

$$S(t) = 4 + 3 \sin 100 \pi t + 5 \sin 200 \pi t$$

I understand that, for the sine wave with same frequency and different amplitude, 

I can use the formula 

$$\sin (\omega t)+ A_{2}\sin (\omega t)=(A_{1}+A_{2})\sin (\omega t)$$

but how to add sine wave that has different frequency ? 

Thanks!
You can't add two sines of different frequencies.
This is a fundamental limit which much of math and physics takes advantage of.

Its also the basis of the fourier transform.

To put it simply, sines of different frequencies are orthogonal.
You can't add two sines of different frequencies.
This is a fundamental limit which much of math and physics takes advantage of.

Its also the basis of the fourier transform.

To put it simply, sines of different frequencies are orthogonal.