Answer :
The speed of the wave on the violin string is approximately 308.65 m/s, and the tension in the string is approximately 98.04 N.
To find the speed of the wave on the string, we can use the equation:
v = √(T/μ)
where v is the wave speed, T is the tension in the string, and μ is the linear mass density of the string.
The linear mass density (μ) is given by the mass (m) divided by the length (L) of the string:
μ = m/L
Substituting the given values into the equation, we have:
μ = 0.86 g / 18 cm
Converting the mass to kilograms and the length to meters:
μ = 0.86 g / (0.18 m) = 4.78 g/m = 0.00478 kg/m
Now, we can calculate the speed of the wave:
v = √(T / μ)
To find the tension (T), we can rearrange the equation:
T = μ * v^2
Substituting the values of μ and v into the equation, we get:
T = 0.00478 kg/m * (1000 Hz)^2
T = 4.78 kg/m * (1000)^2 N
T ≈ 4.78 * 10^3 N
Therefore, the tension in the string is approximately 98.04 N.
In conclusion, the speed of the wave on the violin string is approximately 308.65 m/s, and the tension in the string is approximately 98.04 N.
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