Final answer:
Propagation speed is the rate at which a wave moves through a medium and is determined by the medium's properties, while frequency is how often the wave cycles pass a point per unit time. They are related through the equation v = f × λ, indicating that wavelength changes if either propagation speed or frequency changes, assuming the other stays constant. Therefore, both affect wavelength but are independent of each other.
Step-by-step explanation:
Difference Between Propagation Speed and Frequency
The propagation speed of a wave is the rate at which the wave moves through a medium. It is determined by the properties of the medium (i.e., elasticity, density) and is usually denoted by the symbol 'v'. On the other hand, frequency is the number of cycles of the wave that pass a point in a unit of time, measured in hertz (Hz) and represented by the symbol 'f'. These two factors, propagation speed and frequency, are related to the wavelength of the wave through the equation v = f × λ, where λ (lambda) represents wavelength.
Wavelength can be affected by both propagation speed and frequency. If the propagation speed is constant, which is common in a given medium, the wavelength is inversely proportional to the frequency. This means that as frequency increases, the wavelength decreases, and vice versa while keeping the speed constant. The equation shows that any change in frequency or propagation speed, assuming the other variable remains constant, would result in a change in wavelength.
Implications for Mechanical Waves
For a mechanical wave, such as a wave on a string, the propagation speed might depend on the tension and the linear mass density of the string. However, the frequency at which the wave oscillates is a separate characteristic and does not directly affect propagation speed. When dealing with mechanical waves, if you alter the conditions of the medium (for example, changing the tension in the string), the propagation speed will change, and so might the wavelength, assuming the frequency at which you generate the wave remains the same.
Thus, the correct answer to the question is: c) Propagation speed and frequency are independent; Both affect wavelength.