Physics 101 UBC LO 7-8 on beats. Made using powerpoint.

1. Physics 101 LO7/8 Vivian Tsang
14153143

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

3. D1(0, t)=sin(10pit) D2(0, t)=sin(12pit)
D(0, t)=sin(10pit)+sin(12pit)

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