A guitar string has an overall length of 1.28 m and a total mass of 50 g. Once on the guitar, there is distance of 71 cm between its fixed end points. It is tightened to a tension of 810 N. What the wave speed for the waves on the tightened string in m/s?
To find the wave speed for the waves on the tightened string, we need to use the formula:
wave speed (v) = √(tension (T) / linear mass density (µ))
First, let's calculate the linear mass density (µ) of the string. The linear mass density is the mass per unit length of the string and can be calculated using the formula:
linear mass density (µ) = total mass (m) / length (L)
Given that the total mass of the string is 50 g and the overall length is 1.28 m, we can convert the mass to kilograms and apply it to the formula:
linear mass density (µ) = (50 g) / (1.28 m) = 0.0391 kg/m (approximately)
Next, we have the tension (T) of the string, which is given as 810 N.
Now, we can substitute these values into the equation:
wave speed (v) = √(T / µ)
wave speed (v) = √(810 N / 0.0391 kg/m)
Calculating this result gives:
wave speed (v) ≈ √(20714.07 m²/s²)
Finally, we can determine the square root value:
wave speed (v) ≈ 143.94 m/s
Therefore, the wave speed for the waves on the tightened string is approximately 143.94 m/s.