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 \(v = f\lambda\) (where \(v\) is wave - speed, \(f\) is frequency, and \(\lambda\) is wavelength) shows that for a constant \(v\) (waves are traveling at the same speed), \(f=\frac{v}{\lambda}\). So, a smaller wavelength means a higher frequency.

Step2: Compare the wavelengths of the two waves

Count the number of wavelengths in a given position range. For the first graph (upper graph), assume we count the number of full - cycle repetitions (from one point on the wave to the same point on the next cycle) over the \(x\) (position) range. Let's say over the \(x\) range from \(x = 0\) to \(x=10\) cm, we can see more full - cycle repetitions (shorter wavelength) compared to the second graph (lower graph).

Answer:

The upper graph has a greater frequency.