Two guitars are playing together producing a beat frequency. The first guitar is playing at a frequency of 867 Hz and the beat is produced every 0.04 seconds. What are some possible frequencies the other guitar could be playing to make this beat?

875 Hz or 860 Hz

904 Hz or 830 Hz

878 Hz or 856 Hz

892 Hz or 842 Hz

892 Hz or 842 Hz

Explanation:

Given

The frequency of first guitar is 867 Hz

Beat is produced for every 0·04 s

∴ Beat has a time period of 0·04 s

Beat frequency is defined as the inverse of the time period of the beat

Beat frequency = 1 : (Time period) = 1 : 0·04 = 25 Hz

Let the frequency of the second guitar be f Hz

Beat frequency is defined as the absolute difference between the two frequencies

∴ Beat frequency = (867 - f) or (f - 867)

First case

25 = 867 - f ⇒ f = 842 Hz

Second case

25 = f - 867 ⇒ f = 892 Hz

∴ Possible frequencies of second guitar could be 892 Hz or 842 Hz