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To solve the problem about the speed of the wave traveling through the guitar string, we will use the following formula for wave speed on a stretched string:

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

Where:
- \( v \) is the speed of the wave.
- \( T \) is the tension in the string (in Newtons).
- \( \mu \) is the linear mass density of the string (mass per unit length), given by \( \mu = \frac{m}{L} \), where \( m \) is the mass of the string, and \( L \) is the length of the string.

From the problem:
- \( L = 0.63 \, \text{m} \)
- \( m = 0.17 \, \text{kg} \)
- \( T = 71 \, \text{kg} \, \text{m/s}^2 = 71 \, \text{N} \)

Now let's calculate the linear mass density \( \mu \) and then the wave speed \( v \).The speed at which the wave travels through the guitar string is approximately **16.22 m/s**.

Would you like more details or have any further questions?

Here are 5 related questions:
1. How would increasing the tension in the string affect the wave speed?
2. What happens to the wave speed if the mass of the string increases?
3. How does the length of the string impact the wave speed?
4. Can this formula be applied to other types of waves, such as sound waves?
5. How do different materials affect the wave speed in a string?

**Tip**: The tension in the string plays a crucial role in determining wave speed, and small changes in tension can have significant effects!

A guitar string is 0.63 m long and weighs 0.17 kg. If it is under 71 Kg m/s^2 of tension, what speed does the wave travel at?

Learn how to calculate the speed of a wave traveling through a guitar string that is 0.63 meters long, weighs 0.17 kg, and is under 71 N of tension. This problem explores wave mechanics and the relationship between tension and linear mass density.

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