Two musicians are comparing their trombones. The first produces a tone that is known to be 438 Hz. When the two trombones play together they produce 6 beats every 2 seconds. Which statement is true about the second trombone?

a.It is producing a 444-Hz sound, and could be producing no other sound frequency.
b.It is producing either a 436-Hz sound or a 440-Hz sound.
c.It is producing either a 435-Hz sound or a 441-Hz sound.
d.It is producing either a 432-Hz sound or a 444-Hz sound.
e.It is producing a 441-Hz sound, and could be producing no other sound frequency.

Beat is a phenomenon of interference that occurs when two waves with slightly different frequency interfere with each other. When this occurs, the frequency of the beats is given by

[tex]f_B = |f_1 -f_2|[/tex] (1)

where f1, f2 are the frequencies of the two waves.

In this problem, we have 6 beats every 2 seconds, so the beat frequency is

[tex]f_B = \frac{6}{2 s}=3 Hz[/tex]

We also know the frequency of one of the two sounds,

[tex]f_1 = 438 Hz[/tex]

So according to eq.(1), this means that the sound of the second trombone can have 2 different frequencies:

[tex]f_2 ' = f_1 + f_B = 438 Hz + 3 Hz = 441 Hz\\f_2 '' = f_1 - f_B = 438 Hz - 3 Hz = 435 Hz[/tex]