Wavelengths of two notes in the air are `((70)/(153))m` and `((70)/(157))m`. Each of these notes produces `8` beats per second with a tuning fork of fixed frequency . Find the velocity of sound in the air and frequency . Find the velocity of sound in the air and frequency of the tuning fork.

Explanation

Given: `lambda_(1)=((70)/(153))m`
`lambda_(2)=((70)/(157))m`
`v=?`
`n=?`
`lambda_(1) gt lambda_(2)`
So, `n_(1) lt n_(2)`
`n_(1) lt n lt n_(2)`
`n_(2)=n+8` and `n_(1)=n-8`
`:.n_(2)-n_(1)=16` [Using equation `(i)`]
`(v)/(lambda_(2))-(v)/(lambda_(1))=16`
`v[(157)/(70)-(153)/(70)]=16`
`v[0.057]=16`
`v=280m//s`
For two notes in air, `n_(1)lambda_(1)=n_(2)lambda_(2)`
`(n-8)((70)/(153))=(n+8)((70)/(157))` [Using equation `(i)`]
`implies (n-8)/(153)=(n+8)/(157)`
`implies157(n-8)=153(n+8)`
`implies4n=2480`
`impliesn=620Hz`.