A steel wire of length 1 m, mass 0.1 kg and uniform cross-sectional area 1 0 − 6 m² is rigidly fixed at both ends. The temperature of the wire is lowered by 20°C. If transverse waves are set up by plu

Question

A steel wire of length 1 m, mass 0.1 kg and uniform cross-sectional area $1 0^{- 6}$ m² is rigidly fixed at both ends. The temperature of the wire is lowered by 20°C. If transverse waves are set up by plucking the string in the middle, calculate the frequency of the fundamental mode. $Y = 2 \times 1 0^{11}$ N/m², $α = 1.21 \times 1 0^{- 5}$ /°C. (answer in $Hz$ ).

Answer:

11

Solution:

Tension $T = Y A α Δ T = 2 \times 1 0^{11} \times 1 0^{- 6} \times 1.21 \times 1 0^{- 5} \times 20 = 48.4$ N. $μ = 0.1$ kg/m. $v = 484 = 22$ m/s. $f = v /2 L = 11$ Hz.

TestHub · Accepted Answer

Tension T = Y A α Δ T = 2 × 1 0 11 × 1 0 − 6 × 1.21 × 1 0 − 5 × 20 = 48.4 N. μ = 0.1 kg/m. v = 484 ​ = 22 m/s. f = v /2 L = 11 Hz.

Physics - Wave on String Question with Solution | TestHub

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