Question

The velocity of the transverse wave in a given string is given by v = (T/u)^1/2, where T is tension and u is mass per unit length. In an experiment the weight applied is 3.0 kg, length of the string is 1.000 m and mass of string is 2.5 g. what is the percentage error in the measurement of velocity?

Answer 1

v = √T / √μ                           μ = m / L

Percentage error in μ = 100 * Δμ/μ
 = 100 * Δm/m + 100 * ΔL/L
 = 100 * 0.1/2.5 +100 * 0.001/1.000 = 4.1


percentage error = 100* Δv/v
 = 100 *1/2 * ΔT/T + 100 * 1/2 * Δμ /μ 
 = 50 * 0.1 / 3.0  + 1/2 * 4.1
 = 1.667 +2.05 
 = 3.7