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 is \(v = f\lambda\), where \(v\) is speed, \(f\) is frequency, and \(\lambda\) is wavelength. Given that \(v\) is the same for both waves (\(v_1=v_2\)), so \(f_1\lambda_1 = f_2\lambda_2\). Frequency \(f\) and wavelength \(\lambda\) are inversely - proportional (\(f=\frac{v}{\lambda}\)).

Step2: Analyze the wavelength from the graphs

Wavelength \(\lambda\) is the distance between two consecutive crests (or troughs) of a wave. Looking at the first graph, the wavelength is larger (more distance between consecutive crests or troughs). Looking at the second graph, the wavelength is smaller.

Step3: Determine the frequency

Since \(f=\frac{v}{\lambda}\) and \(v\) is constant. If \(\lambda_1>\lambda_2\), then \(f_1 < f_2\) (because when the denominator \(\lambda\) is smaller, the value of the fraction \(f\) is larger for a fixed \(v\)). So the second graph (the one with the smaller wavelength) has a greater frequency.

Answer:

The second graph (the lower - one in the given problem) has the greater frequency.