A tuning fork of frequency 256 Hz produces 4 beats per second when sounded with a stringed instrument. What is the frequency produced by the instrument?

Explanation

`n = ( c_(17))/( 2I)` where `I = "length of the pipe"`
`:. 256 - ( c_(17))/( 2I) = 4 or ( c_(17))/(2 I) = 252`
Since beats decrease first and then increase to `4` , then the frequency of the pipe increases . This can happen only if the temperature increases.
Let `t` be the final temperature , in Celsius.
Now ` (c_(t))/( 2 I) - 252 = 4 or (c_(t))/( 2I) = 260`
Dividing `( c_(t))/( c_(17)) = (260)/(252)`
or `sqrt ((273 + t)/( 273 + 17)) = (260)/(252)` `( c prop sqrt(T))`
or ` t = 308.7 - 273 = 35.7^(@) C`
`:.` Rise in temperature ` = 35.7 - 17 = 18.7 ^(@) C`