Answer :
Final answer:
The question involves finding the mass that allows an oscillator to produce the fourth harmonic on a string, which requires understanding the relationship between tension, mass, and frequency for harmonics. The provided information is not sufficient to calculate the exact mass without additional numerical details.
Explanation:
The student is asking about the fourth harmonic in a simple harmonic oscillator setup, specifically about the mass required for the oscillator to produce this harmonic on a string. This question relates to the concept of standing waves on a stretched string and involves understanding the relationship between tension, mass, and frequency for harmonics.
We can use the formula for the frequency of the nth harmonic of a stretched string, which is f = (n/2L) * sqrt(F/μ), where f is the frequency, n is the harmonic number, L is the length of the string, F is the tension, and μ is the linear mass density (mass per unit length of the string).
To answer the question about which mass m would allow the oscillator to set up the fourth harmonic, we would need to rearrange this formula to solve for the tension F, given the frequency and linear mass density, and then use the tension to determine the necessary mass that would provide that tension. However, without specific numerical values for frequency and string length, we cannot calculate the exact mass.
