A piano string having a mass per unit length equal to 5.00 „e 10¡V3 kg/m is under a tension of 1 350 N. Find the speed with which a wave travels on this string.
wave speed = sqrt[T/(mass per length)]
A piano string having a mass per unit length equal to 5.00x 10.3 kg/m is under a tensional 1350 n. find the speed ofa wave traveling in this string
To find the speed with which a wave travels on the string, we can use the formula for wave speed:
v = sqrt(T/µ)
where v is the wave speed, T is the tension in the string, and µ is the mass per unit length of the string.
Given:
Mass per unit length (µ) = 5.00 x 10^-3 kg/m
Tension (T) = 1,350 N
Substituting these values into the formula, we have:
v = sqrt(1,350 N / 5.00 x 10^-3 kg/m)
To simplify the calculation, let's express the mass per unit length in kg/m as follows:
5.00 x 10^-3 kg/m = 5.00 x 10^-3 * 1000 g/m = 5.00 g/m
Now we can plug in the values:
v = sqrt(1,350 N / 5.00 g/m)
Calculating this expression gives:
v ≈ sqrt(270 N·m / g) ≈ sqrt(270 m^2/s^2)
Taking the square root of 270 m^2/s^2, we find:
v ≈ 16.43 m/s
Therefore, the speed at which the wave travels on this piano string is approximately 16.43 m/s.