The equation of a wave on a string of linear mass density $0.02 \text{kg m}^{-1}$ is $Y = 0.01sin[2π(\frac{t}{0.02}-\frac{x}{0.50})]$ m. The tension in the string is

Question

A steel wire with mass per unit length $ 7.0 \times 10^{-3} \, \text{kg/m} $ is under a tension of $ 70 \, \text{N} $. The speed of transverse waves in the wire will be:

Answer 1

Step 1: Approach
Use the ratio of angular frequency to wave number.

Step 2: Values
$\omega=\dfrac{2\pi}{0.02}=100\pi$ rad/s and $k=\dfrac{2\pi}{0.50}=4\pi$ rad/m. So $v=\omega/k=25$ m/s.

Step 3: Tension
$T=\mu v^2=0.02\times25^2=12.5$ N. Option (A).

Final Answer:
The wave speed is 25 m/s, so the tension is 0.02 times 625 = 12.5 N, option (A). \[ \boxed{12.50\ \text{N}} \]

The equation of a wave on a string of linear mass density \(0.02 \text{kg m}^{-1}\) is \(Y = 0.01sin[2π(\frac{t}{0.02}-\frac{x}{0.50})]\) m. The tension in the string is

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The Correct Option is A

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