Two identical piano wires, kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beat's when both the wires oscillate together would be

Question

Two identical piano wires, kept under the same tension T have a fundamental frequency of 600 Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beat's when both the wires oscillate together would be (A) 0.01 (B) 0.02 (C) 0.03 (D) 0.04

Tardigrade Admin · Accepted Answer

As v=(1/2 L) √(T/μ) ∴ (Δ v/v)=(1/2) (Δ T/T) (Δ T/T)=2 (Δ v/v)=2 × (6/600)=0.02

Q. Two identical piano wires, kept under the same tension $T$ have a fundamental frequency of $600 Hz$ . The fractional increase in the tension of one of the wires which will lead to occurrence of $6$ beat's when both the wires oscillate together would be

0.01

0.02

0.03

0.04

As $v = \frac{1}{2 L} \frac{T}{μ}$
$∴ \frac{Δ v}{v} = \frac{1}{2} \frac{Δ T}{T}$
$\frac{Δ T}{T} = 2 \frac{Δ v}{v} = 2 \times \frac{6}{600} = 0.02$

Q. Two identical piano wires, kept under the same tension T have a fundamental frequency of 600Hz. The fractional increase in the tension of one of the wires which will lead to occurrence of 6 beat's when both the wires oscillate together would be