Frequency Math Example 4

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

hard

Two tuning forks produce tones modeled by

y_1 = \sin(880\pi t)

and

y_2 = \sin(884\pi t)

. Find the beat frequency when both are played together.

1
Frequencies: $f_1 = \frac{880\pi}{2\pi} = 440$ Hz and $f_2 = \frac{884\pi}{2\pi} = 442$ Hz.
2
The beat frequency is $|f_2 - f_1| = |442 - 440| = 2$ Hz. You hear 2 beats (volume pulsations) per second.

Answer

\text{Beat frequency} = 2 \text{ Hz}

When two waves with slightly different frequencies are combined, the resulting amplitude oscillates at the beat frequency

|f_1 - f_2|

. This is because

\sin(A) + \sin(B) = 2\sin\frac{A+B}{2}\cos\frac{A-B}{2}

— the cosine factor creates the 'beating' effect. Musicians use beats to tune instruments.

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].

A sound wave completes [formula] cycles per second. Find the period and write a sine function modeli

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