A string with a length of 2.5m resonates in five loops. The string linear density is 0.05 kg/m and the suspended mass is 0.5 kg.
To determine the speed of the waves traveling on the string, we can use the formula:
v = √(T/μ)
Where:
v is the speed of the wave,
T is the tension in the string, and
μ is the linear density of the string.
First, let's calculate the tension (T) in the string using the suspended mass (m) and the acceleration due to gravity (g):
T = m * g
In this case, the suspended mass is 0.5 kg, and we can assume the acceleration due to gravity to be approximately 9.8 m/s².
T = 0.5 kg * 9.8 m/s²
T = 4.9 N
Next, we substitute the tension (T) and the linear density (μ) into the formula:
v = √(T/μ)
In this case, the linear density (μ) is 0.05 kg/m.
v = √(4.9 N/0.05 kg/m)
To calculate the speed of the waves, we need to convert Newtons to kg/m:
1 N = 1 kg * m/s²
4.9 N = 4.9 kg * m/s²
v = √(4.9 kg * m/s² / 0.05 kg/m)
v = √(98 m²/s²)
v ≈ 9.90 m/s
Therefore, the speed of the waves traveling on the string is approximately 9.90 m/s.