How many wave cycles are completed in this diagram? 85 waves or
Waves Worksheet Name: Date: Period: b) Wavelength
c) Amplituse
d) frequency
e.) speed
The Correct Answer and Explanation is:
Correct Answer:
a) How many wave cycles are completed in this diagram?
Answer: 8.5 wave cycles (or 8 and 1/2)
Explanation
To determine how many wave cycles are completed in the diagram, we must understand what a wave cycle is. A wave cycle refers to one complete oscillation of the wave — typically measured from one crest to the next crest or from one trough to the next trough.
Looking at the image, we observe a sinusoidal wave, which means it has repeating crests (peaks) and troughs (valleys). The green and black waveform shown in the diagram is counted at the top, from left to right, with numbers marking full cycles: 1, 2, 3, …, up to 8. After the 8th full cycle, we see half of another wave—either a crest or a trough—indicating 0.5 of a cycle.
So, by counting the number of full wave cycles and the extra half wave at the end, we get:
- 8 full cycles
- + 0.5 of a cycle
= 8.5 wave cycles total
It’s important to distinguish wave cycles from wave crests or troughs. A full cycle consists of both a crest and a trough. If you were counting only peaks or only valleys, you might overestimate or underestimate.
This information is vital in wave mechanics because the number of wave cycles over a given distance or time affects calculations for frequency, wavelength, and wave speed. For example, if we know the frequency (number of cycles per second) and the wavelength (length of one cycle), we can find the speed of the wave using the formula:Speed=Wavelength×Frequency\text{Speed} = \text{Wavelength} \times \text{Frequency}Speed=Wavelength×Frequency
According to the worksheet:
- Wavelength = 10 cm
- Frequency = 8 Hz
So, speed would be:Speed=10 cm×8 Hz=80 cm/s\text{Speed} = 10 \, \text{cm} \times 8 \, \text{Hz} = 80 \, \text{cm/s}Speed=10cm×8Hz=80cm/s
Understanding how to count wave cycles accurately is foundational in physics, especially in the study of sound, light, and electromagnetic waves.
