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A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of 45Hz. The mass of the wire is 3.5 × 10-2kg and its linear mass density is 4.0 × 10-2kgm-1. What is1. the speed of a transverse wave on the string and2. the tension in the string? |
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Answer» mass of wire M = 3.5 × 10-2kg Linear density µ = mass / length = M/l = 4.0 × 10-2kg ∴ Length of wire l = \(\frac{M}{μ}\)=\(\frac{3.5×10^{−2}} {4 \times 10^{-2}}\)m = 0.875m In the fundamental mode, λ =2l = 2 × 0.875m = 1.75m 1. Speed of transverse waves u = v λ = 45 × 1.75ms-1 = 78.75ms-1 2. u= \(\sqrt{\frac{T}{μ}}\) or T = µu2 = 4 × 10-2(78.75)2N = 278.06N. |
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