Question

A water wave is created in a wave tank. It has an amplitude of 3 and a period of 4pi/5. Find the equation of this wave as a sine function.

Answer 1

Answer:
`y=3sin((5)/(2)x)`

Explanation:

1. You know the following equation of sine function:

`y=Asin(B(x+C))+D`

2. Where:

A is the amplitude.

`B=(2\pi)/(period)`

C is phase shift and D is vertifcal shift

3. C and D are zero. Then:

`A=3\\B=(2\pi)/((4\pi)/(5))=(5)/(2)`

4. Substitute these values into the equation:

`y=3sin((5)/(2)x)`