Answer :
The speed of waves on the violin string is approximately 14.04 m/s.
To find the speed of waves on a violin string, we can use the formula for wave speed on a string:
[tex]\[ v = \sqrt{\frac{T}{\mu}} \][/tex]
where:
- v is the speed of waves on the string,
- T is the tension in the string,
- μ is the linear mass density of the string.
Given:
- Mass of the string (m) = 599 mg = 0.599 g = 0.000599 kg
- Length of the string (L) = 20.8 m
First, we need to calculate the linear mass density (\( \mu \)) of the string, which is given by:
μ = m/L
μ = 0.000599 / 20.8
μ = 2.88 × 10⁻⁵ kg/m
Next, we need to determine the tension in the string. The tension in the string can be calculated using the formula:
T = μ . g . L
where:
g is the acceleration due to gravity (approximately 9.81 m/s²).
T = 2.88 × 10⁻⁵ . 9.81 . 20.8
T = 0.00568 N
Now, we can calculate the speed of waves on the violin string using the formula:
v = [tex]\sqrt{\frac{T}{\mu}}[/tex]
v [tex]= \sqrt{\frac{0.00568}{2.88 \times 10^{-5}}[/tex]
v = √197.22
v ≈ 14.04 m/s
Therefore, the speed of waves on the violin string is approximately 14.04 m/s.
