At a temperature of `27^(@) C`, two identical organ pipes produce notes of frequency 140 Hz. If the temperature of one pipe is raised to `57.75^(@)`, then the number of beats produced pre second is

Options

A. 7
B. 5
C. 3
D. 9

Answer

A

Explanation

Here, `n_(0) = 140 Hz, T_(0) = 27^(@)C= 300K` and
`T_(2) = 57.75^(@)C = 330.75K`
The variation of speed of sound with temperature,
`v_(t)/v_(0)=sqrt(T/T_(0))`
Let `v_(0) = `speed of sound at the room temperature.
`v_(t) = v_(0)sqrt((330.75)/300) = 1.05 v_(0)` Hence, the beats produced in oragan pipe.
Number of beats, `n+ n_(1) - n_(0) = 140 xx 1.05 - 140 =7`
`( because n_(1) = v_(t)/(4L) and n_(0) = v_(0)/(4L))`
So, the correct option is (a).