Trigonometric functions

[bully3000]

A sound wave has frequency 50 Hz (i.e. it has wavelength/period=0.02 seconds). Within each beat, the highest sound intensity is 100 decibel (dB) and the lowest intensity is 60 dB. Supposing that t=0 corresponds to the low intensity, write down a trigonometric function which describes this sound wave. Sketch the sound wave over two periods.

Any help will be appreciated!

[Zealous]

Sort of ran out of time to type everything out in full steps, but you should be able to get the idea if you've done a bit of trig modelling.

General form of trig graphs:
or
(excluding translations horizontally)

Anyway, they've already told you the period is to be 0.02 seconds (and we're assuming t is in seconds).

Period of a sin/cos graph is , where b is the coefficient of x within sin/cos.

So let and solve for b.

The amplitude is half the distance between the maximum and minimum decibels, so solve for a accordingly.
C should generally be halfway between the maximum and minimum.

Now it sounds like by saying "t=0 corresponds to the low intensity", the minimum of the graph sits at t=0. If you know what sin/cos graph look like, you can probably match that with a cos graph reflected in the x-axis.

Spoiler

The final answer will be probably something like: