Final answer:
The slope of the frequency and wavelength graph conveys the inverse relationship between frequency and wavelength, demonstrated by the equation v = fλ, which indicates the product of wavelength and frequency is constant for a given wave speed.
Step-by-step explanation:
The slope of the frequency and wavelength graph represents the relationship between frequency (f) and wavelength (λ). Since the speed of light (v) is constant, the relationship v = fλ indicates that frequency and wavelength are inversely related. When plotted on a standard graph, this inverse relationship results in a downward sloping curve. However, on a log-log plot, which is often used to graph the relationship between wave properties, the inverse relationship can appear as a straight line with a negative slope.
The constant product of wavelength and frequency across different data points in Table 17.1 and the consistent product of frequency times air column height as shown in the problem statement both support this inverse relationship.