The equation of a wae is represented by $y=10^{-4} \sin \Bigg(100t -\frac{x}{10}\Bigg)m, $ then the velocity of wave will be

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

Let's solve the problem step by step to find the velocity of the wave. The given wave equation is:

y = 10^{-4} \sin \Bigg(100t - \frac{x}{10}\Bigg)

This wave equation can be compared with the standard wave equation y = A \sin(\omega t - kx), where:

A is the amplitude
\omega is the angular frequency
k is the wave number

From the given wave equation, we can identify:

\omega = 100
k = \frac{1}{10}

The formula for the velocity v of a wave is given by:

v = \frac{\omega}{k}

Substitute the values of \omega and k we obtained:

v = \frac{100}{\frac{1}{10}} = 100 \times 10 = 1000 \, \text{m/s}

Thus, the velocity of the wave is 1000 m/s.

Conclusion: Among the given options, the correct answer is 1000 m/s.

Answer 2