Question

wave properties review directions: answer the question about wavelength. what is the wavelength of the wave above? blank meters

Explanation:

Step1: Identify wavelength definition

Wavelength is the distance between two consecutive identical points (e.g., crests or troughs) on a wave.

Step2: Locate consecutive points

Find two consecutive crests (or troughs). For example, the first crest is at \( x = 1 \) m (approx), the next at \( x = 3 \) m? Wait, no, looking at the graph, the wave crosses the x - axis at 0, then at 2, 4, 6, 8. Wait, actually, the distance between two consecutive peaks (or two consecutive zero - crossings in the same direction). Let's take the points where the wave crosses the x - axis going up: at \( x = 0 \), \( x = 2 \)? No, wait, no. Wait, the wavelength is the distance between two identical points. Let's look at the peaks. The first peak is around \( x = 1 \), the next at \( x = 3 \)? No, wait the graph has marks at 0, 2, 4, 6, 8. Wait, from \( x = 0 \) to \( x = 4 \), how many wavelengths? Wait, no, let's see the distance between two consecutive troughs or crests. Let's take the point where the wave starts at (0,0), then the next time it's at (4,0) going up? Wait, no, the wave pattern: from 0 to 4, is that one wavelength? Wait, no, actually, the distance between two identical points. Let's count the number of units. The graph has x - axis marks at 0, 2, 4, 6, 8. The wave repeats every 4 meters? Wait, no, looking at the wave, from the origin (0,0) to the point (4,0) where the wave is in the same phase (going up), the distance is 4 meters? Wait, no, wait the wavelength is the distance between two consecutive peaks. Wait, maybe a better way: the distance between two consecutive points where the wave has the same phase. For example, the first peak is at \( x = 1 \) (approx), the next at \( x = 5 \)? No, that can't be. Wait, looking at the graph, the wave has a period (wavelength) of 4 meters? Wait, no, let's check the x - axis. The marks are at 0, 2, 4, 6, 8. The wave crosses the x - axis at 0, then at 2, 4, 6, 8. Wait, the distance between 0 and 4 is 4 meters, and in that distance, how many wavelengths? Wait, no, actually, the wavelength is the distance between two consecutive crests or troughs. Let's take the troughs: the first trough is at \( x = 3 \) (approx), the next at \( x = 7 \)? No, that's not right. Wait, maybe I made a mistake. Wait, the graph is a wave, and the wavelength is the distance between two identical points. Let's look at the x - axis labels: 0, 2, 4, 6, 8. The wave from 0 to 4: the distance from 0 to 4 is 4 meters, and in that interval, how many wavelengths? Wait, no, actually, the wavelength is 4 meters? Wait, no, let's see: from \( x = 0 \) to \( x = 4 \), the wave completes one full cycle? Wait, no, a full cycle of a wave is from peak to peak, trough to trough, or zero - crossing to zero - crossing in the same direction. Let's take the zero - crossing going up: at \( x = 0 \), then at \( x = 4 \), then at \( x = 8 \). So the distance between \( x = 0 \) and \( x = 4 \) is 4 meters, which is the wavelength. Wait, but let's check the number of waves. From 0 to 8, there are two full waves? Wait, no, from 0 to 4 is one wavelength, 4 to 8 is another. So the wavelength is 4 meters. Wait, but let's count the distance between two consecutive peaks. The first peak is at \( x = 1 \), the next at \( x = 5 \)? No, that's 4 meters. Yes, so the wavelength is 4 meters. Wait, but looking at the graph, the distance between 0 and 4 is 4 meters, and that's one wavelength. So the wavelength is 4 meters.

Answer:

\( 4 \)