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 the speed of the wave, \(f\) is the frequency, and \(\lambda\) is the wavelength) shows that when \(v\) is constant (given that the waves are traveling at the same speed), \(f=\frac{v}{\lambda}\). So, a smaller wavelength means a larger frequency.

Step2: Compare the wavelengths of the two waves

Count the number of full - wave cycles in a given distance interval (say from \(x=- 10\) to \(x = 10\)).

• For the left - hand graph: There are more full - wave cycles in the interval from \(x=-10\) to \(x = 10\).
• For the right - hand graph: There are fewer full - wave cycles in the interval from \(x=-10\) to \(x = 10\).

Since the left - hand graph has a smaller wavelength (more cycles in the same distance interval), and \(f=\frac{v}{\lambda}\) (\(v\) is constant), the left - hand graph represents the wave with a greater frequency.

Answer:

The left - hand graph.