Question

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

Explanation:

Step1: Identify wave cycles

From the graph, count the number of full wave cycles between two points. Let's take from 0 to 8 meters. The number of full cycles here is 8 (since each cycle repeats at intervals). Wait, no, actually, let's check the distance between two consecutive crests or troughs. Wait, looking at the x - axis (distance in meters), from 0 to 2 meters, how many cycles? Wait, no, let's see the markings. The x - axis has marks at 0, 2, 4, 6, 8. Let's count the number of wavelengths between 0 and 8. Wait, each wavelength is the distance between two consecutive identical points (like crest to crest or trough to trough). Let's see, from 0 to 2 meters, how many cycles? Wait, no, let's count the number of waves in 8 meters. Wait, the graph shows that in 8 meters, there are 8 waves? No, wait, let's look at the peaks. The first peak is at around 0.5, then next at 1.5, then 2.5, 3.5, 4.5, 5.5, 6.5, 7.5. Wait, no, maybe the distance between two consecutive peaks (wavelength) is 1 meter? Wait, no, let's check the x - axis. The distance from 0 to 8 meters, and how many wavelengths? Wait, the key is to find the distance between two consecutive identical points. Let's take the distance between two points where the wave crosses the x - axis in the same direction. For example, at x = 0, it crosses upwards, then next at x = 1, then x = 2, etc. Wait, maybe the wavelength is 1 meter? Wait, no, let's calculate. The total distance is 8 meters, and how many wavelengths? Looking at the graph, from 0 to 8 meters, there are 8 wavelengths? Wait, no, let's count the number of cycles. Wait, the wave has a peak - trough - peak pattern. Let's count the number of peaks. From 0 to 8 meters, how many peaks? Let's see, the first peak is near 0.5, then 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5. So that's 8 peaks in 8 meters. So the distance between two consecutive peaks (wavelength, $\lambda$) is $\frac{8\space m}{8}=1\space m$? Wait, no, wait, maybe I made a mistake. Wait, let's take the distance between two consecutive crests. The first crest is at x = 0.5, the next at x = 1.5, so the distance between them is 1.5 - 0.5 = 1 meter. So the wavelength is 1 meter. Wait, but let's check the x - axis markings. The x - axis has major ticks at 0, 2, 4, 6, 8. So between 0 and 2, how many wavelengths? If we look at the wave, from 0 to 2 meters, there are 2 wavelengths? No, that can't be. Wait, maybe the correct way is: the formula for wavelength when we know the total distance (d) and the number of waves (n) is $\lambda=\frac{d}{n}$. From the graph, the total distance d = 8 meters, and the number of waves n = 8 (since from 0 to 8, there are 8 full waves). So $\lambda=\frac{8\space m}{8}=1\space m$. Wait, but let's confirm. Another way: the distance between two consecutive identical points (like two crests) is the wavelength. Looking at the graph, the distance between two crests is 1 meter (since from x = 0.5 to x = 1.5 is 1 meter, which is one wavelength).

Step2: Calculate wavelength

Using the formula $\lambda=\frac{\text{Total Distance}}{\text{Number of Wavelengths}}$. The total distance along the x - axis is 8 meters, and the number of wavelengths in 8 meters is 8 (by counting the number of full wave cycles). So $\lambda=\frac{8\space m}{8} = 1\space m$.

Answer:

1