A tuning fork of frequency 256 Hz and an open organ pipe of slightly lower frequency are at 17^(@) C. When sounded together , they produce4 beats. On altering that the number of beats per second first diminshes to in what direction has the temperature of the air in thepipe been altered ?

A tuning fork of frequency 256 Hz and an open organ pipe of slightly l

1.	A tuning fork of frequency 256 Hz and an open organ pipe of slightly lower frequency are at 17^(@) C. When sounded together , they produce4 beats. On altering that the number of beats per second first diminshes to in what direction has the temperature of the air in thepipe been altered ?
Answer» Solution :`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`