Question

Two out-of-tune flutes play the same note. One produces a tone that has a frequency of 248 Hz, while the other produces 288 Hz. When a tuning fork is sounded together with the 248-Hz tone, a beat frequency of 20.0 Hz is produced. When the same tuning fork is sounded together with the 288-Hz tone, a beat frequency of 20.0 Hz is produced. What is the frequency of the tuning fork

Answer 1

F = 268 Hz

Step-by-step explanation:

The beat frequency is given as:

`Beat Frequency = |Frequency 1 - Frequency 2|\\`|

So, for the first flute and tuning fork:

`20 Hz = |248 Hz - F|`

where,

F = Frequency of tuning fork

F = 248 Hz ± 20 Hz

F = 268 Hz (OR) 228 Hz

Now, for the second flute and tuning fork:

`20 Hz = |288 Hz - F|`

where,

F = Frequency of tuning fork

F = 288 Hz ± 20 Hz

F = 268 Hz (OR) 308 Hz

Since, 268 Hz is common from both calculations. Therefore, it will be the frequency of the tuning fork.

F = 268 Hz