Frequency Math Example 2

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

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A sound wave completes

440

cycles per second. Find the period and write a sine function modeling this wave with amplitude

1

1
Frequency $= 440$ Hz means $440$ cycles per second, so the period is $T = \frac{1}{440}$ seconds.
2
The angular frequency is $\omega = 2\pi f = 2\pi(440) = 880\pi$ radians per second.
3
The function is $y = \sin(880\pi t)$ , where $t$ is in seconds.

Answer

y = \sin(880\pi t), \quad T = \frac{1}{440} \text{ s}

In applications, frequency is often measured in Hertz (Hz = cycles per second). The angular frequency

\omega = 2\pi f

converts from cycles to radians. The note A above middle C has frequency

440

Hz — this is the standard tuning pitch used by orchestras.

About Frequency

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

Find the period and frequency of [formula].

Find the period of [formula].

Two tuning forks produce tones modeled by [formula] and [formula]. Find the beat frequency when both