A piano string having a mass per unit length equal to `5.00 xx 10^(3)kg//m` is under a tension of `1350 N`, Find the speed with which a wave travels on this string.

Explanation

To find the speed of a wave traveling on a piano string, we can use the formula:

\[ v = \sqrt{\frac{T}{\mu}} \]

where:
- \( v \) is the speed of the wave,
- \( T \) is the tension in the string,
- \( \mu \) is the mass per unit length of the string.

### Step-by-step Solution:

1. **Identify the given values:**
- Mass per unit length (\( \mu \)) = \( 5.00 \times 10^{-3} \, \text{kg/m} \)
- Tension (\( T \)) = \( 1350 \, \text{N} \)

2. **Substitute the values into the formula:**
\[ v = \sqrt{\frac{T}{\mu}} = \sqrt{\frac{1350 \, \text{N}}{5.00 \times 10^{-3} \, \text{kg/m}}} \]

3. **Calculate the denominator:**
\[ \mu = 5.00 \times 10^{-3} \, \text{kg/m} = 0.005 \, \text{kg/m} \]

4. **Perform the division:**
\[ \frac{T}{\mu} = \frac{1350 \, \text{N}}{0.005 \, \text{kg/m}} = 270000 \, \text{m}^2/\text{s}^2 \]

5. **Take the square root to find the speed:**
\[ v = \sqrt{270000} \approx 519.62 \, \text{m/s} \]

### Final Answer:
The speed of the wave traveling on the piano string is approximately \( 519.62 \, \text{m/s} \).