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=nlamda`, if `v` increases n will increase at `27^@C`, `v_1=nlamda`, at `31^@C`,`v_2=(n+x)lamda`
Now using `vpropsqrtT` (because`v=sqrt((gammaRT)/(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))impliesx=2`
`[:.(1+x)^(n) =1 +nx]`.