Question

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

Explanation:

Step1: Recall the definition of wavelength

Wavelength is the distance between two consecutive crests (or troughs) of a wave.

Step2: Analyze the first graph

Count the number of wavelengths in a given position range. For the first graph, in the range from \(x = - 10\) to \(x=10\), there are more cycles (more crests/troughs in the same \(x -\) range).

Step3: Analyze the second graph

In the second graph, in the range from \(x=-10\) to \(x = 10\), there are fewer cycles. Since wavelength \(\lambda=\frac{\text{total distance}}{\text{number of wavelengths in that distance}}\), and the total distance (\(x = 10-(-10)=20\) in both cases). If \(n\) (number of wavelengths) is smaller, \(\lambda\) is larger.

Answer:

The second graph has the greater wavelength.