Question

the graphs below describe two waves. the waves are traveling at the same speed. select the graph of the wave with the greater frequency.

Explanation:

Step1: Recall the relationship between frequency and wavelength

The formula for wave speed \(v = f\lambda\), where \(v\) is speed, \(f\) is frequency, and \(\lambda\) is wavelength. Given \(v\) is the same for both waves (\(v_1=v_2\)), so \(f_1\lambda_1 = f_2\lambda_2\). Then \(f=\frac{v}{\lambda}\), which means frequency is inversely proportional to wavelength (\(f\propto\frac{1}{\lambda}\)).

Step2: Compare the wavelengths of the two waves

Count the number of wavelengths in a given position range. For the left - hand graph, in a certain position range (say from \(x = - 10\) to \(x=10\)), there are more wave cycles (higher number of crests and troughs in the same spatial interval) compared to the right - hand graph. A smaller wavelength \(\lambda\) implies a higher frequency \(f\) (since \(f=\frac{v}{\lambda}\) and \(v\) is constant).

Answer:

The left - hand graph (the graph with more wave cycles in the same position range) has the greater frequency.