A piano string having a mass per unit length equal to 5.10 10-3 kg/m is under a tension of 1,500 N. Find the speed with which a wave travels on this string.
Wave Speed = √[T/Mass per length]
To determine the speed at which a wave travels on the piano string, you can use the wave speed equation:
v = √(T/μ)
where:
v is the wave speed
T is the tension in the string
μ is the linear mass density (mass per unit length) of the string.
In this case, the tension (T) is given as 1,500 N, and the linear mass density (μ) is given as 5.10 × 10^(-3) kg/m.
Substituting the given values into the equation:
v = √(1,500 N / 5.10 × 10^(-3) kg/m)
Calculating the value:
v = √(1,500 / (5.10 × 10^(-3)))
Now, simplify the expression:
v = √(1,500 / (0.00510))
v = √(294,117.65)
v ≈ 542.50 m/s
Therefore, the speed with which a wave travels on this piano string is approximately 542.50 m/s.