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 wave speed formula

The wave speed formula is \(v = f\lambda\), where \(v\) is the speed, \(f\) is the frequency, and \(\lambda\) is the wavelength. Given that \(v\) is the same for both waves (\(v_1=v_2\)), we have \(f_1\lambda_1 = f_2\lambda_2\), so \(f=\frac{v}{\lambda}\).

Step2: Analyze the wavelength from the graphs

From the graphs, the wave on the left has a shorter wavelength (\(\lambda\)) compared to the wave on the right.

Step3: Determine the frequency relationship

Since \(f=\frac{v}{\lambda}\) and \(v\) is constant, a smaller \(\lambda\) implies a larger \(f\).

Answer:

The graph of the wave on the left has the greater frequency.