Beats: A person is hearing two sound waves simultaneously. One has a period of 1.50 ms and the other one a period of 1.54 ms. What is the period of the beat due to these two waves?
A) 0.040 ms
B) 1.5 ms
C) 3.0 ms
D) 58 ms
E) 330 ms

Question

Quizplus · Accepted Answer

The beat frequency (f_beat) is the absolute difference between the frequencies of the two waves. First, convert the periods (T) given in milliseconds to seconds (since 1 ms = 1e-3 s), then use the formula f = 1/T to find the frequencies. For the first wave, T1 = 1.50 ms = 1.50e-3 s, so f1 = 1/T1 = 1/(1.50e-3) Hz. For the second wave, T2 = 1.54 ms = 1.54e-3 s, so f2 = 1/T2 = 1/(1.54e-3) Hz. The beat frequency is |f1 - f2|. After calculating f1 and f2, find the beat frequency, then convert it back to a period (T_beat = 1/f_beat) to find the period of the beat in seconds, and finally convert it back to milliseconds if necessary. The calculation shows that the beat period is closest to the option D, 58 ms.

Beats: a Person Is Hearing Two Sound Waves Simultaneously