Question

A guitar string produces 4 beats/second when sounded with

a250Hz tuning fork and 9 beats/second when sounded with a 255
Hztuning fork. What is the vibrational frequency?

Answer 1

In first case vibrational frequency will be 246 Hz and 254 Hz

In second case vibrational frequency will be 264 Hz and 246 Hz

Step-by-step explanation:

We have given a guitar produces 4 beats per second when sounded with 250 Hz and produce 9 beats per second when sounded with 255 Hz

Expression of beat frequency is
`beat\ frequency=\left | f_1-f_2 \right |`

Here
`f_1` is vibrational frequency

So
`4=\left | f_1-250 \right |`

`f_1-250=\pm 4`

`f_1=254,246Hz`

For second case

`9=\left | f_1-255 \right |`

`f_1-250=\pm 9`

`f_1=264,246Hz`