PHYSICS 101 beat Frequency

1. BEATS
BY: NANCY MANHAS

3. BEATS - AN INTRODUCTION
• Wave interference occurs when two individual
waves meet along the same medium; resulting
in two major types of phenomena, destructive
and constructive interference
• Constructive interference can be described as a
meeting between two of the exact same pulses
at an upward-upward/downward-downward
position
• Destructive interference can be described as a
meeting between two of the exact same
sinusoidal pulses at an upward-downward
position
• Alternating constructive and destructive
interferences, produces an soft-loud-soft module
that is interpreted as beats

4. BEAT FREQUENCY-
APPLICATIONS
Scenario 1:
Kevin is tuning his guitar strings. After finishing his E4 string to a
frequency of 280Hz, he begins to adjust the B3 string. When
Kevin strikes the two strings together, he hears 12 beats every 4
seconds. As well, he notices that the frequency of the B3 string is
higher than the frequency of the E4 string. Determine the
frequency of the B3 string.

5. SOLUTION #1:
• In order to solve this
question, we must first
understand that the beat
frequency is an average of
the frequencies. fbeat = favg =
f1 - f2
• What the observer hears is
the absolute value
difference between these
two frequencies, |f1 - f2|

6. • Since we know that in order for a beat frequency to occur the two
frequencies between the waves must be nearly the same
• Therefore, we can make an assumption that our second frequency will be
similar to that of our first one.
• Using the following equation, beat f = |f1 - f2|, we can find out what the frequency
of the second string is
• First, the equation tells us that the frequency hear is 12 beats every 4 seconds, the
beat frequency can be determined
• fbeat = # of beats/time : 12 beats/4 seconds = 3Hz is heard every second to the
observer.
• We now know fbeat, and can now determine the frequency of the B3 string, using
the following formula: beat f = |f1 - f2|

7. SOLUTION CONTINUED…
• beat f = |f1 - f2| f1 = 280 Hz
+/- 3Hz = 280Hz - f2
Since the frequency can either be +/- 3, due to no indication delivered by beats (shown by the absolute value brackets), we
must determine both the above or below frequencies:
+3 Hz = 280Hz - f2
f2 = 280Hz - 3Hz
f2 = 277 Hz
-3 Hz = 280 Hz - f2
f2 = 280 - (-3Hz)
f2 = 280 + 3Hz
f2 = 283 Hz

8. • Therefore, f2 of the B3 string is either 283Hz or 277Hz
• However, since we are told that Kevin noticed the B3 string to have
a higher frequency when strung, the B3 string must be of higher
value.
• As a result the B3 string must be 283Hz, in order for it to
synonymous to the definition of a beat frequency.

9. CITATIONS
• http://hyperphysics.phy-
astr.gsu.edu/hbase/sound/beat.html
• http://www.physicsclassroom.com/class/sound/Lesso
n-3/Interference-and-Beats
• Nelson Textbook: Physics for Scientists and
Engineers (Revised custom of Volume 1)