3. a custom car built for pretentious people has two brass horns that are supposed to produce the same frequency but actually emit 267.8 and 266.4 hz. what beat frequency is produced?

When two waves with different frequencies combine, two new waves are created, with frequencies at the sum and difference of the two original ones.  The new ones are called the 'beats'.

Original two frequencies:  267.8 Hz,  266.4 Hz .

Beat at the sum  =      (267.8 + 266.4)  =  534.2 Hz .

Beat at the difference = (267.8 - 266.4)  =  1.4 Hz .

In this situation, we're typically not aware of the sum-beat at 534 Hz.
Our consciousness is flooded with the two original frequencies, and
with hearing the whole combined sound going "wah wah wah" at
1.4 times per second.  But the 534-Hz note is there too ... part of
what makes the whole thing sound so ragged and discordant.