Two identical flutes produce fundamental notes of frequency `300Hz` at `27^@C`. If the temperature of air in one flute is increased to `31^@C`, the number of the beats heard per second will be

Options

A. 1
B. 2
C. 3
D. 4

Answer

B

Explanation

Velocity of sound increases if the temperature increases. So, with `v=n lambda`, if v increases n will increase.
at `27^(@)C,v_(1)=n lambda`, at `31^(@)C`,
`v_(2)=(n+x)lambda`
Now, using `v prop sqrt(T)(because v=sqrt((lampbda"RT")/(M))`
`(v_(2))/(v_(1))=sqrt((T_(2))/(T_(1)))=(n+x)/(n)`
`implies" "(300+x)/(300)=sqrt(((273+31))/((273+27)))`
`=sqrt((304)/(300))=sqrt((300+4)/(300))`
`implies1+(x)/(300)=(1+(4)/(300))^(1//2)`
`=(1+(1)/(2)xx(4)/(300))`
`implies" "x=2" "[because(1+x)^(n)=1+nx]`