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 is the difference between the frequencies of the two waves. First, convert the periods (T) given in milliseconds to frequencies (f) using the formula f = 1/T. For the first wave, f1 = 1/(1.50 ms) = 666.67 Hz, and for the second wave, f2 = 1/(1.54 ms) = 649.35 Hz. The beat frequency is the absolute difference between these two, which is |666.67 Hz - 649.35 Hz| = 17.32 Hz. The period of the beat is then the reciprocal of the beat frequency, Tbeat = 1/fbeat = 1/17.32 Hz ≈ 0.0578 seconds or 57.8 ms, which rounds to 58 ms when considering the given options.

A Person Is Hearing Two Sound Waves Simultaneously