Transverse waves with a speed of 55.0 m/s are to be produced on a stretched string. A 5.05 m length of string with a total mass of 0.0600 kg is used.
Calculate the wave speed in the string if the tension is 8.00 N.
To calculate the wave speed in the string, we can use the equation:
v = √(T/μ)
Where v is the wave speed, T is the tension, and μ is the linear mass density.
First, let's calculate the linear mass density (μ) of the string. The linear mass density is given by the mass per unit length, so we can find it by dividing the total mass of the string by its length:
μ = m/L
where μ is the linear mass density, m is the total mass of the string, and L is the length of the string.
μ = 0.0600 kg / 5.05 m
≈ 0.0119 kg/m
Next, we can substitute the values of T and μ into the equation to calculate the wave speed:
v = √(T/μ)
= √(8.00 N / 0.0119 kg/m)
≈ √672.27 N/(kg/m)
≈ 25.93 m/s
Therefore, the wave speed in the string is approximately 25.93 m/s.