It looks like you've uploaded an image of a mathematical problem. Please allow me a moment to review and extract the relevant details so I can assist you further.The problem in the image is a physics-based math question related to tension in a wire, particularly under the effect of wind. Here is the transcription of the problem:

A wire 1.0 m long with a mass of 0.015 kg is suspended between two poles. When the wind blows, it applies a force of 0.030 N on the wire. If the tension in the wire is 60 N, what is the speed of the transverse wave produced in the wire?

Options: (a) 55.6 m/s
(b) 63.2 m/s
(c) 69.3 m/s
(d) 75.0 m/s

To solve this, we'll use the formula for the speed of a transverse wave on a string, which is:

$v = \sqrt{\frac{T}{\mu}}$

where:

• $v$ is the wave speed,
• $T$ is the tension in the string (60 N),
• $\mu$ is the linear mass density, given by $\mu = \frac{m}{L}$ where $m$ is the mass of the wire (0.015 kg) and $L$ is its length (1.0 m).

Let me calculate the result for you.The speed of the transverse wave in the wire is approximately $63.2 \, \text{m/s}$.

Thus, the correct answer is (b) 63.2 m/s.

Would you like further details or have any questions? Here are five follow-up questions to deepen your understanding:

1. What factors affect the speed of a wave on a string?
2. How does tension in the wire impact the wave speed?
3. What is linear mass density, and how is it used in wave mechanics?
4. How would the wave speed change if the mass of the wire were doubled?
5. Why doesn't the applied wind force affect the wave speed directly?

Tip: When solving wave problems on strings, always ensure the correct calculation of linear mass density before applying the wave speed formula.