# Some questions about sound(sine) waves.

1. Feb 20, 2014

### ZooBooBooZoo

Hi all.

I'm a music student and I've been trying to educate myself about acoustics lately.

I'm exploring the correlations between two pure sound waves.
This might be more of a mathemetical question rather than a physics one but anyways:

I want to know how can I calculate when/how freuqently this function:
f(x)=sin(x)+sin(1.05x)
will be zeroed.

I wanna know this so I can now know frequent the pulses occur(by pulses I mean the fluctuating volume of the sound).

Also, what is the proper way to define the sine function of , say, 440Hz?
Sin(440) ?

Thx in advance, hope I'm not too noobish :)

2. Feb 20, 2014

### maajdl

Use the relation Sin(a) + Sin(b) = 2 Cos((a-b)/2) Sin((a+b)/2)

If you have a sound at frequency f = 440Hz, the pressure varies in time (t) like

Sin(2*∏*f* t) = Sin(ω* t)

or

Sin(2*∏*f* t + shift) = Sin(ω* t + shift)

Usually, one defines ω=2*∏*f.

Concerning your signal and the beats, you will get from above:

f(ω t) = Sin(ω t) + Sin(1.05 ω t) = 2 Cos(0.025 ω t) Sin(1.025 ω t)

From this, you can see when the wave f(ω t) goes to zero.
It does that at a high frequency because of the second factor Sin(1.025 ω t).
But the whole high-frequency wave is modulated by the first factor Cos(0.025 ω t) which goes to zero at a lower frequency.