Frequency Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Find the period and frequency of f(x)=sinโก(4x)f(x) = \sin(4x).

Solution

  1. 1
    For f(x)=sinโก(Bx)f(x) = \sin(Bx), the period is T=2ฯ€โˆฃBโˆฃT = \frac{2\pi}{|B|}.
  2. 2
    Here B=4B = 4, so T=2ฯ€4=ฯ€2T = \frac{2\pi}{4} = \frac{\pi}{2}.
  3. 3
    Frequency is the reciprocal of the period: f=1T=2ฯ€f = \frac{1}{T} = \frac{2}{\pi} cycles per unit.

Answer

T=ฯ€2,f=2ฯ€T = \frac{\pi}{2}, \quad f = \frac{2}{\pi}
Frequency measures how many complete cycles occur per unit of the independent variable. A higher BB value compresses the wave horizontally, increasing the frequency and decreasing the period. Frequency and period are always reciprocals of each other.

About Frequency

The number of complete wave cycles passing a fixed point per second, measured in hertz (Hz).

Learn more about Frequency โ†’

More Frequency Examples