Final answer:
The frequency of the first harmonic on a taut string fixed at both ends depends on the length, mass, and tension of the string. Temperature indirectly affects the frequency through changes in tension.
Step-by-step explanation:
The frequency of the first harmonic set up on a taut string, fixed at both ends, depends on several factors, including the length of the string, the mass of the string, and the tension in the string. The fundamental frequency, or first harmonic, can be calculated using the formula f₁ = v / (2L), where f₁ is the fundamental frequency, v is the speed of the wave on the string, and L is the length of the string. The speed of the wave on the string (v) is related to the tension (T) and the linear mass density (μ) of the string according to the equation v = √(T/μ). As the tension increases, the speed of the wave and therefore the frequency increase. Also, as the mass of the string increases, which affects the linear mass density, or if the length of the string increases, the frequency decreases. The temperature of the string typically does not affect the first harmonic frequency directly, but it can indirectly affect the tension in the string, thereby altering the frequency.