A laboratory experiment uses a single uniform string of length 1.20m fixed at both ends. The string is kept vibrating by a signal generator set permanently to a frequency of 120Hz. By slowly adjusting the tension, the experimenter observes strong resonances (large‐amplitude standing waves) at two different tension values.
• When the tension is 13N, exactly five antinodes are seen along the string.
• When the tension is increased to 37N, exactly three antinodes are seen.
Assume the linear mass density of the string remains constant.
(1) Identify the harmonic number corresponding to each observed resonance and explain your reasoning.
(2) Develop an algebraic expression for the linear mass density μ of the string in terms of the fixed frequency f, the string length L, the harmonic number n, and the corresponding tension T. Do not substitute numerical values yet.
(3) Using your expression from part (b) and the two tension–harmonic data points provided, calculate μ for the string.
(4) Predict the tension at which a resonance with exactly two antinodes would occur for the same driving frequency of 120Hz. Show all steps in your calculation.