# Answer in Physics for Earl #163233

Two speakers are set simultaneously in the auditorium. The two speakers are set with different frequency. If the first speaker is 267Hz and the other is 273 Hz. Determine the beat frequency and the observed frequency heard by crowd.

(a) We can find the beat frequency as follows:

“f_{beat}=|f_2-f_1|=|273 Hz-267 Hz|=6 Hz.”

(b) If two sounds differ in frequencies, the sound waves can be modeled as:

“y_1=Acos(k_1x-2pi f_1t), y_2=Acos(k_2x-2pi f_2t).”

Using the trigonometric identity

“cosu+cosv=2cos(dfrac{u+v}{2})cos(dfrac{u-v}{2})”

and considering the point in space as “x=0 m” we find the resulting sound at a point in space, from the superposition of the two sound waves:

“y(t)=2Acos(2pi f_{avg}t)cos(2pi(dfrac{|f_2-f_1|}{2})t),”

here, “f_{avg}=dfrac{f_1+f_2}{2}” is the observed frequency heard by crowd.

Then, we get:

“f_{obs}=f_{avg}=dfrac{273 Hz+267 Hz}{2}=270 Hz.”

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