Question

Plot another sin function of 20% higher frequency over the same range.

Answer 1

Explanation:

The frequency of sine function is given by the number of periods in a given range. For example:

• Frequency for
  `sin(x)` is 1 in the interval
  `[0,2\pi]`.

This means that, if we want another sine function with frequency 20% higher, we need that function to have a frequency of 1.2 in the interval
`[0,2\pi]`.

To be easier to see we will consider interval
`[0,10\pi]` instead of
`[0,2\pi]`. In this interval
`sin(x)` has 5 periods, therefore our new sine function should have 6 periods.

Finally, as we can see in the graph, the function
`sin((6)/(5)x )` (in blue) has a frequency 20% higher than
`sin(x)` (in red). This can be easily seen counting the number of periods between 0 and
`10\pi` for both functions. 5 for
`sin(x)` and 6 for
`sin((6)/(5) x)`.