Question

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

Answer 1

Step-by-step 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 $sin(\frac{6}{5}x )$ (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 $sin(\frac{6}{5} x)$.