Calculate the speed of a wave travelling along a stretched string that is under a tension of50 N and has a mass per unit length of 3.110–4 kg m–1
Question
Calculate the speed of a wave travelling along a stretched string that is under a tension of 50 N and has a mass per unit length of 3.1 × 10<sup>–4</sup> kg m<sup>–1</sup>.
Solution
The speed of a wave (v) traveling along a stretched string can be calculated using the formula:
v = sqrt(T/μ)
where: T is the tension in the string (in Newtons) μ is the mass per unit length of the string (in kg/m)
Given: T = 50 N μ = 3.1 x 10^-4 kg/m
Substituting these values into the formula, we get:
v = sqrt(50 / 3.1 x 10^-4)
To simplify this, we first calculate the denominator:
50 / 3.1 x 10^-4 = 161290.32
Then, we take the square root of this result:
v = sqrt(161290.32) = 401.61 m/s
So, the speed of the wave traveling along the string is approximately 401.61 m/s.
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