What factors determine the frequency of a note emitted by a vibrating string?

Analyze the question: We need the factors that determine the frequency of a note from a vibrating string (like a guitar or sonometer wire).

Concept: For a stretched string fixed at both ends, the fundamental frequency is

f = (1/2L) × √(T/μ)

where:

• L = length of the string
• T = tension in the string
• μ = mass per unit length of the string

Step by step:

1. The formula contains only L, T and μ, so these three factors determine the frequency.
2. Amplitude does not appear in the formula. Plucking a string harder makes the note louder, not higher in pitch. This eliminates options A and B.
3. "Force constant" (as in Hooke's law) is not a variable in the string frequency formula. This eliminates option D.
4. Option C lists mass per unit length, tension and length, which matches the formula exactly.

Answer: Option C is correct.

Tip: Remember the three variables as L-T-μ: length, tension and mass per unit length.

• Shorter string → higher frequency
• Greater tension → higher frequency
• Heavier (thicker) string → lower frequency

This is why thick guitar strings give bass notes and tightening a string raises its pitch. Amplitude only affects loudness, never pitch.