Question

When String A is played with String B, itcreates a 1.0 Hz beat frequency. WhenString A is played with String C, itcreates a 2.0 Hz beat frequency. If youplay String B and C together, what beatfrequency will they make? (There aretwo possible answers; give one.)(Unit = Hz)

Answer 1

Given:

Frequency produced by String A and B = 1.0 Hz.

Frequency produced by String A and C = 2.0 Hz.

Let's find the frequency produced by string B and C.

Apply the formula:

`f_(21)=|f_2-f_1|`

Now, for the frequency produced by A and B, we have:

`\begin{gathered} f_(BA)=|f_B-f_A| \\ \\ 1.0=f_B-f_A \\ \end{gathered}`

For the frequency produced by A and C, we have:

`\begin{gathered} f_(CA)=|f_C-f_A| \\ \\ 2.0=f_C-f_A \end{gathered}`

Now, we have the system of equations:

1.0 = fB - fA

2.0 = fC - fA

Let's solve both equations simultaneously.

Rewrite the first equation for fA:

fA = fB - 1.0

Substitute (fB - 1.0) for fA in the second equation:

2.0 = fC - (fB - 1.0)

2.0 = fC - fB + 1.0

2.0 - 1.0 = fC - fB

1.0 = fC - fB

Therefore, the beat frequency string B and string C will make when played together is 1.0 Hz.

• ANSWER:

1.0 Hz.