Two oscillators are started simultaneously in same phase. After 50 oscillations of one, they get out of phase by π, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest to

Question

Two oscillators are started simultaneously in same phase. After 50 oscillations of one, they get out of phase by π, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest to (A) 2 % (B) 1 % (C) 0.5 % (D) 0.25 %

Tardigrade Admin · Accepted Answer

50 T1=(50-0.5) T2 (50/v1)=(49.5/v2) (v1/v2)=(50/49.5) ⇒ ((v1-v2/v2)) × 100 %=((50-49.5/49.5)) × 100 % (Δ v/v) × 100 % ≈ 1 %

Q. Two oscillators are started simultaneously in same phase. After 50 oscillations of one, they get out of phase by $π$ , that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest to

$2%$

$1%$

$0.5%$

$0.25%$

$50 T_{1} = (50 - 0.5) T_{2}$
$\frac{50}{v _{1}} = \frac{49.5}{v _{2}}$
$\frac{v _{1}}{v _{2}} = \frac{50}{49.5}$
$\Rightarrow (\frac{v _{1} - v _{2}}{v _{2}}) \times 100% = (\frac{50 - 49.5}{49.5}) \times 100%$
$\frac{Δ v}{v} \times 100% \approx 1%$

Q. Two oscillators are started simultaneously in same phase. After 50 oscillations of one, they get out of phase by π, that is half oscillation. The percentage difference of frequencies of the two oscillators is nearest to

2%

1%

0.5%

0.25%