2. Two waves with slightly different frequencies
will combine at some point so that their
crests or troughs coincide
When this happens, a maximum sound is heard
because the displacement is at its maximum
When the waves go out of phase, the
amplitude of the resultant waves decreases
When this happens, a minimum sound is heard
because the displacement is at zero
Beats are the periodic variation of sound
levels that occur when two waves of slightly
different frequencies interfere
4. The number of times the sound level is at its
maximum in one second
Beat Frequency=the difference between the
two frequencies
fbeat=I f1-f2 I
5. The human ear can only differentiate
between a beat frequency of 10 beats per
second
fbeat=I f1-f2 I < 10
After this level, the two waves go
periodically in and out of phase and our ears
are not sensitive enough to detect the
differences
6. Two tuning forks of frequencies 200Hz and
204 Hz are struck so that they simultaneously
produce sound waves
What is the beat frequency ?
7. fbeat=I f1-f2 I
Let f1= 200Hz
Let f2= 204Hz
fbeat=I 200-204 I
fbeat=I -4 I
fbeat= 4Hz
8. A cellist is tuning the middle C (262 Hz)
string on his cello by listening for beats when
this note is played with a tuning fork at the
frequency desired. He hears 5 beats per
second and notices that when he decreases
the tension in the string slightly, the beat
frequency degreases. What was the
frequency of the out of tune string?
9. A) 253Hz
B) 224Hz
C) 267Hz
D) 273Hz
E) 257Hz
10. C) 267Hz
Reason:
The beat frequency is found to be 5Hz
This is because the cellist hears 5 beats per
second when he tunes his instrument
According to fbeat=I f1-f2 I, the cello must be 5Hz
off from the middle C frequency of 262Hz
When he decreases the tension, the beat
frequency decreases which means that the
instrument is getting more in-tune (less beats
heard)
11. Therefore, because we know that decreasing
string tension also decreases the frequency of
the string’s oscillation, we can deduct that the
original frequency of the string must be higher
by 5 Hz compared to middle C