Final answer:
The mass m needed to change the frequency of a vibrating string on a sonometer from 30 Hz to 50 Hz is calculated using the formula relating tension and frequency. After solving the equation, the value is determined to be 72 g.
Step-by-step explanation:
The question is about determining the mass needed to change the fundamental frequency of a vibrating string on a sonometer from 30 Hz to 50 Hz. This can be solved using the relationship between the frequency of vibration, the mass causing the tension, and the physical properties of the string. The frequency of a vibrating string is proportional to the square root of the tension and inversely proportional to the square root of the linear mass density and the length of the string (which are constants in this experiment).
Given that the frequency when a 180 g mass is attached is 30 Hz, the frequency when the mass m is attached and is 50 Hz can be found using the formula: f₁/f₂ = √(m₂/m₁), where f₁ and f₂ are the frequencies, and m₁ and m₂ are the respective masses causing the tensions.
To find the unknown mass m, we rearrange the formula to solve for m₂: m₂ = m₁ * (f₁²/f₂²). Substituting the known values, m₂ = 180 g * (30 Hz)² / (50 Hz)² = 180 g * 0.36 / 0.25 = 72 g.
So, the value of the mass m that needs to be attached to change the fundamental frequency to 50 Hz is 72 g.