Lisa is standing on a dock beside a lake. She drops a rock from her hand into the lake. After the rock hits the surface of the l
ake, the rock's distance from the lake's surface changes at a rate of −4 inches per second. If Lisa holds her hand 5 feet above the lake's surface, how far from Lisa's hand is the rock 2 seconds after it hits the surface?
The frequency of sine function is given by the number of periods in a given range. For example:
Frequency for is 1 in the interval .
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 .
To be easier to see we will consider interval instead of . In this interval has 5 periods, therefore our new sine function should have 6 periods.
Finally, as we can see in the graph, the function (in blue) has a frequency 20% higher than (in red). This can be easily seen counting the number of periods between 0 and for both functions. 5 for and 6 for .