Question

Two identical sonometer wires have fundamental frequencies of 500 vibration/sec, when
kept under the same tension. What fractional increase in the tension of one wire would
cause an occurrence of 5 beats per second. When both wires vibrate together?
Options:
1. 1.020
2. 1.20
3. 0.20
4. 0.020​

Answer 1

Explanation:

Given Two identical sonometer wires have fundamental frequencies of 500 vibration/sec, when kept under the same tension. What fractional increase in the tension of one wire would  cause an occurrence of 5 beats per second. When both wires vibrate together?  

• So the difference in frequency Δf = 5 beats / sec
• So the difference between two nodes is λ / 2. Let this be equal to L
•                           So λ/2 = L
•                            Or λ = 2 L
• So frequency f = v / λ
•            Now velocity v = √T / μ
•            So f = 1/2L √T / μ
• Squaring we get
•                    f^2 = 1/4L^2 (T/μ)
• Differentiating we get
•              2 Δf / f = ΔT / T
• We need to find ΔT/T
•            So Δf = 5
•            f = 500 hz
• So ΔT / T = 2 x 5/500
•               = 1/50
• So fractional increase will be 1/50 = 0.02

Reference link will be

https://brainly.in/question/10251691