A Level Physics Practice Exam

What is the equation for fundamental frequency in relation to tension and mass?

1. f = 1/2L(root(Tension / Mass))

2. f = 2L(root(Tension / Mass))

3. f = 1/L(root(Tension * Mass))

4. f = L(root(Tension / Mass))

The correct answer is: f = 1/2L(root(Tension / Mass))

The fundamental frequency of a vibrating string is directly related to the tension in the string and its mass per unit length. The correct formula for the fundamental frequency is derived from the principles of wave mechanics and is given by: \[ f = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \] Where: - \( f \) is the fundamental frequency, - \( L \) is the length of the string, - \( T \) is the tension in the string, - \( \mu \) is the mass per unit length of the string. The mass per unit length \( \mu \) can be expressed as the total mass \( m \) divided by the length \( L \) of the string; thus, \( \mu = \frac{m}{L} \). Rearranging the equation leads to the conclusion that \( f \) is inversely proportional to the length of the string and directly proportional to the square root of the tension divided by the mass per unit length. This demonstrates that the fundamental frequency increases with tension and decreases with increasing mass, showcasing the relationship effectively. In this context, option A correctly captures this relation by including the factor \( \frac{1}{2L