Final answer:
The speed of a mechanical wave depends primarily on the properties of the medium, including its density and elasticity, and is independent of the amplitude or wavelength. The correct answer to what the speed of a mechanical wave depends on is option c) Frequency and medium properties.
Step-by-step explanation:
The speed of a mechanical wave depends on various factors, predominantly the properties of the medium through which it travels. This includes the density, elasticity, and temperature of the medium. Unlike electromagnetic waves, mechanical waves require a medium to propagate and the characteristics of this medium play a pivotal role in determining the wave's speed.
When considering the relationship between amplitude, frequency, wavelength, and the speed of a wave, it is essential to understand that the amplitude of a wave does not affect its speed. Instead, the amplitude is related to the energy and intensity of the wave. The frequency of a wave, which is the number of oscillations per second, is also independent of the wave's speed. Meanwhile, the wavelength is inversely related to the frequency given a constant wave speed. The properties of the medium, such as its elastic properties and mass density, are the key factors that impact the speed of a mechanical wave.
Regarding seismic waves, for example, the speed of these waves will depend on the properties of the Earth's materials through which they propagate, not on the size of the medium. Similarly, in standing waves on a string, such as a guitar string, the frequency depends on the propagation speed and the characteristics of the string, like its density and tension.
In conclusion, the correct option that describes what the speed of a mechanical wave depends on is: c) Frequency and medium properties.