Trigonometric Function Graphs Math Example 4

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

Example 4

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A sound wave has the equation P(t)=0.002sinโก(440ฯ€t)P(t)=0.002\sin(440\pi t) (pressure in Pa, time in seconds). Find the frequency (Hz) and explain the connection to the period.

Solution

  1. 1
    Period: T=2ฯ€440ฯ€=2440=1220T=\frac{2\pi}{440\pi}=\frac{2}{440}=\frac{1}{220} seconds.
  2. 2
    Frequency: f=1/T=220f=1/T=220 Hz. This is the musical note AA below middle CC.
  3. 3
    Connection: frequency is cycles per second == number of complete oscillations in one second =1/period= 1/\text{period}.

Answer

Period =1220=\frac{1}{220} s; Frequency =220=220 Hz
In wave physics, period and frequency are reciprocals: f=1/Tf=1/T. The bb parameter in sinโก(bt)\sin(bt) equals 2ฯ€f2\pi f (angular frequency). Higher frequency means shorter period โ€” the wave completes more cycles per second.

About Trigonometric Function Graphs

The graphs of sinโกx\sin x, cosโกx\cos x, and tanโกx\tan x as functions of a real variable, characterized by amplitude, period, phase shift, and vertical shift.

Learn more about Trigonometric Function Graphs โ†’

More Trigonometric Function Graphs Examples

Example 1 easy

Identify the amplitude, period, phase shift, and vertical shift of [formula]. Write in standard form

Example 2 hard

Write the equation of a cosine function with amplitude [formula], period [formula], phase shift righ

Example 3 easy

State the amplitude and period of each: (a) [formula], (b) [formula], (c) [formula].

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