Final answer:
The frequency of standing waves on a string depends on the tension and the mass per unit length (linear density) of the string, not the amplitude or medium density. The wave speed, central to frequency determination, is a function of these physical properties and is essential in the creation of standing waves.
Step-by-step explanation:
In standing waves on a string, the frequency of vibration is determined by several factors relating to the physical properties of the string and the force applied to it. Specifically, the frequency depends on the tension in the string and its mass per unit length, also known as the linear density. This is because the speed of wave propagation is proportional to the square root of the tension divided by the linear density (v = √(T/μ)). The frequency can also be related to the wavelength (λ) and the speed (v) of the wave through the equation f = v/λ, where f is the frequency.
Amplitude does not affect the frequency of standing waves, but rather is related to the energy and intensity of the wave. Furthermore, in the context of this question, while the medium's density can affect the speed of sound waves traveling through a fluid, the density of a string does not play a direct role in affecting the frequency of standing waves on that string. Instead, it is the mass per unit length that is pertinent. To calculate the speed of a wave on a string and consequently determine the frequency of standing waves, the distance between two points on the string (such as two fixed ends), the tension in the string, and, for completeness, the time for a complete oscillation, should be measured.
The wave speed itself is indeed dependent on the characteristics of the medium, such as the tension and linear density of a string, as those determine how quickly a disturbance can travel through it, influencing the frequency of the wave produced. Frequency and wavelength are therefore critically linked to these physical properties and the force exerted to establish the wave, whereas amplitude and medium density, in the context of a string, are not directly related to the frequency of standing waves.