Physics 101 LO7/8 Vivian Tsang

14153143

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

D1(0, t)=sin(10pit) D2(0, t)=sin(12pit)

D(0, t)=sin(10pit)+sin(12pit)

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

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

Two tuning forks of frequencies 200Hz and

204 Hz are struck so that they simultaneously

produce sound waves

What is the beat frequency ?

fbeat=I f1-f2 I

Let f1= 200Hz

Let f2= 204Hz

fbeat=I 200-204 I

fbeat=I -4 I

fbeat= 4Hz

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?

A) 253Hz

B) 224Hz

C) 267Hz

D) 273Hz

E) 257Hz

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)

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