two sound waves have frequencies of 12Hz and 10Hz. Calculate their beats period

Analyze the question: Two sound waves with slightly different frequencies combine to produce beats. We need the beat period, which is the time between successive beats.

Concept: The beat frequency is the difference between the two frequencies:

f_beat = |f₁ − f₂|

The beat period is the reciprocal of the beat frequency:

T = 1 / f_beat

Solution:

1. Beat frequency: f_beat = 12 − 10 = 2 Hz
2. Beat period: T = 1 / 2 = 0.5 s

Answer: The beat period is 0.

Tip: Do not stop at the frequency difference. "Beat frequency" and "beat period" are different quantities. If the question asks for the period, always take the reciprocal at the end. Here, 2 Hz is the beat frequency (2 beats per second), but the question asks for the time per beat, which is 0.5 s. Option D (2.0 s) is a common trap, because it is the frequency difference with the wrong unit.