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?
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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
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
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