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

`300 xx (v_0 xx 0.61 xx t_1)/(4l)`
`4l xx 300 = v_0 + 0.61 xx tl`
`4I = 4l xx (v_0 xx 0.61 xx t_1)/(300)`
`f_2 = (v_0 xx 0.61xx t_2)/(v_0 + 0.61 xx t_1) xx 300`
`f_1 - f_2 = ((v_0 xx 0.61 xx t_2 - v_0 - 0.61 xx v_0 - 0.61 xx t_1)300)/(v_0 + 0.61 t_1)`
Beats = `(0.61 xx 4 xx 300)/(v_0 + 0.61 xx 27) = (61 xx 4 xx 3)/(332 + (.61 xx 27))`
`= 2.10061`
So no. of beat Heard = 2