1. 14. Consider the following pairs of frequencies. i. 200 Hz, 304 Hz ii. 303 Hz, 300 Hz iii. 400 Hz,
800 Hz a. Which pair will produce a beat frequency? b. What is the beat frequency? c. Can you
provide any theory as to why a beat frequency sounds unpleasant?
Solution
14) a) answer (ii) ---- 303Hz and 300Hz
b) Beats occur when two frequencies that differ by less than about 15 Hz are sounded together.
Beats are the loudening and softening of the combined sound of the two frequencies. It turns out
that the beat rate is found by subtracting the two frequencies.
c)
Imagine the cone of a loud-speaker vibrating at a given frequency. The motion of the cone
toward the observer produces a compression of the air, which means that the air near the cone
has a pressure higher than atmospheric. This compression moves off at the speed of sound.
Similarly, the motion of the cone away from the observer produces a rarefaction of the air, which
means that the air near the cone has a pressure lower than atmospheric. This rarefaction also
moves off at the speed of sound. When the successive compressions and rarefactions reach the
observer’s ear, they cause the ear drum to move inward and outward, respectively. This
phenomenon causes a perception of a tone, the pitch of which is related to the frequency of
vibration, and the loudness of which is related to the amplitude of the vibration.
What happens when two loud-speakers, side by side vibrate at the same frequency? If they are in
phase (which means that their cones are both moving in the same direction at each instant of
time), their effects add, and a louder sound is heard. This phenomenon is called constructive
interference . If they are out of phase, which means that they are moving in opposite directions at
each instant of time, their effects tend to cancel, and a softer sound is heard. This phenomenon is
called destructive interference .
Now, if the two frequencies of the cones are slightly different, they will be alternately in and out
of phase. Consequently, beats will be heard.