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Question
A steel wire of length 64 cm weighs 5 g. If it is stretched by a force of 8 N, what would be the speed of a transverse wave passing on it?
Solution
Given,
Length of the steel wire = 64 cm
Weight = 5 g
Applied force = 8 N
Thus, we have:
\[\text{ Mass per unit length = \frac{5}{64} gm/cm}\]
\[Tension, T = 8 N\]
\[ = 8 \times {10}^5 dyn\]
\[Speed, v = \sqrt{\left( \frac{T}{m} \right)}\]
\[ = \sqrt{\frac{\left( 8 \times {10}^5 \times 64 \right)}{5}}\]
\[ = 3200 \text{ cm/s = 32 m/s }\]
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