A wire having a linear density of 0.05 g/cm3 is stretched between two rigid supports with a tension of 4.5 × 107 dynes. It is observed that the wire resonates at a frequency of 420 cycles/s. The next higher frequency at which the same wire resonates is 490 cycles/s. Find the length of the wire.
Added by Kathleen V.
Step 1
The linear density is given as 0.05 g/cm³. 1 g/cm³ = 1000 kg/m³, so: \[ 0.05 \, \text{g/cm}^3 = 0.05 \times 1000 \, \text{kg/m}^3 = 50 \, \text{kg/m}^3 \] Show more…
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Two wires are welded together end to end. The wires are made of the same material, but the diameter of one is twice that of the other. They are subjected to a tension of 4.60 $\mathrm{N}$ . The thin wire has a length of 40.0 $\mathrm{cm}$ and a linear mass density of $2.00 \mathrm{g} / \mathrm{m} .$ The combination is fixed at both ends and vibrated in such a way that two antinodes are present, with the node between them being precisely at the weld. (a) What is the frequency of vibration? (b) What is the length of the thick wire?
Two wires are welded together end to end. The wires are made of the same material, but the diameter of one is twice that of the other. They are subjected to a tension of $4.60 \mathrm{N}$. The thin wire has a length of $40.0 \mathrm{cm}$ and a linear mass density of $2.00 \mathrm{g} / \mathrm{m} .$ The combination is fixed at both ends and vibrated in such a way that two antinodes are present, with the node between them being right at the weld. (a) What is the frequency of vibration? (b) What is the length of the thick wire?
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