Calculate the velocity of a transverse wave along a string of length `2 m` and mass `0.06 kg` under a tension of `500 N`.

Explanation

To calculate the velocity of a transverse wave along a string, we can follow these steps:

### Step 1: Calculate the Linear Mass Density (μ)
The linear mass density (μ) is defined as the mass of the string divided by its length.

Given:
- Mass of the string (m) = 0.06 kg
- Length of the string (L) = 2 m

Using the formula:
\[ \mu = \frac{m}{L} \]

Substituting the values:
\[ \mu = \frac{0.06 \, \text{kg}}{2 \, \text{m}} = 0.03 \, \text{kg/m} \]

### Step 2: Use the Formula for Wave Velocity (v)
The velocity (v) of a transverse wave on a string can be calculated using the formula:
\[ v = \sqrt{\frac{T}{\mu}} \]
where:
- T is the tension in the string.

Given:
- Tension (T) = 500 N

### Step 3: Substitute the Values into the Velocity Formula
Now, substituting the values of T and μ into the formula:
\[ v = \sqrt{\frac{500 \, \text{N}}{0.03 \, \text{kg/m}}} \]

### Step 4: Calculate the Velocity
First, calculate the division:
\[ \frac{500}{0.03} = 16666.67 \, \text{m}^2/\text{s}^2 \]

Now, take the square root:
\[ v = \sqrt{16666.67} \approx 129.1 \, \text{m/s} \]

### Final Answer
The velocity of the transverse wave along the string is approximately:
\[ v \approx 129.1 \, \text{m/s} \]

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