Final answer:
The wave speed can be calculated using the linear mass density and tension of the string. In this case, the wave speed is approximately 50.71 m/s.
Step-by-step explanation:
The wave speed for a vibrating string can be found using the linear mass density (μ) and the tension (T) of the string. The equation to calculate the wave speed is:
Wave Speed (v) = √(T/μ)
In this case, the linear mass density is given as 0.00539 grams/cm, which can be converted to kg/m by dividing it by 100. The tension (T) is given as the mass (m) suspended from the end of the string multiplied by the acceleration due to gravity (g).
Substituting the given values into the equation, we have:
v = √((m * g)/μ)
Calculating the values, we get:
v = √((0.0558 kg * 9.80 m/s²)/(0.00539 kg/m)
v ≈ 50.71 m/s
The wave speed on a string can be determined using the string's tension and its linear mass density. After converting the linear mass density to the correct units and calculating the tension with the given mass and gravity, use the formula v = √(T/μ) to find the wave speed.
The question is asking for the wave speed in the vibrating strings experiment. To determine the wave speed for a particular string, you need to know the tension in the string and its linear mass density (μ). In this case, the linear mass density of the string is given as 0.00539 grams/cm, which we first convert to kg/m by multiplying by 0.0001 kg/cm (since 1 g = 0.001 kg, and 100 cm = 1 m). This yields μ = 0.000539 kg/m. The tension (T) in the string is due to the mass suspended from the end, which is 55.8 grams, or 0.0558 kg. Using the acceleration due to gravity (g = 9.80 m/s²), the tension is T = m * g = 0.0558 kg * 9.80 m/s².
The formula for the wave speed (v) on a stretched string is given by v = √(T/μ). After calculating the tension, we can substitute the values for T and μ into this formula to determine the wave speed.