Question

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

Answer 1

It is producing either a 435-Hz sound or a 441-Hz sound.

Step-by-step explanation:

When two sound of slightly different frequencies interfere constructively with each other, the resultant wave has a frequency (called beat frequency) which is equal to the absolute value of the difference between the individual frequencies:

`f_B = |f_1 -f_2|` (1)

In this problem, we know that:

- The frequency of the first trombone is
`f_1 = 438 Hz`

- 6 beats are heard every 2 seconds, so the beat frequency is

`f_B=(6)/(2 s)=3 Hz`

If we insert this data into eq.(1), we have two possible solutions for the frequency of the second trombone:

`f_2 = f_1 - f_B = 438 Hz - 3 Hz = 435 Hz\\f_2 = f_1+f_B = 438 Hz+3 Hz=441 Hz`