Question

Draw a picture of two waves, one with twice the frequency of the other. Label the wave with the higher frequency.

Short answer

First, draw a wave representing the lower frequency. Then, draw a second wave underneath, ensuring this wave features twice as many complete wavelengths within the same timeframe to indicate a frequency double that of the first wave. Lastly, label the second wave as 'Higher Frequency' to clearly indicate the difference.

Step-by-step solution

Draw the first wave

Start by drawing a simple wave. This will represent the wave with the lower frequency. You might want to use a ruler or a straight edge to help keep your drawing neat. Draw a horizontal line to represent time, and then draw a wave pattern above this line.

Draw the second wave with twice the frequency

Next, draw another wave below the first one you drew. This will represent the wave with the higher frequency. To create this wave, make sure you draw two complete wavelengths (a full cycle from peak to peak) for every one wavelength you drew for the first wave. This will show that the frequency of this wave is twice as high.

Label the higher frequency wave

Lastly, label the wave you just drew with 'Higher Frequency'. This makes it clear that this wave has a higher frequency than the first wave you drew. Do not forget to label adequately to avoid any confusion.

Key concepts

Wavelength

When we visualize waves, whether they are sound waves, light waves, or waves on a string, one fundamental property we look at is the wavelength. The wavelength is the distance between two consecutive points that are in phase on a wave, such as crest to crest or trough to trough. In simpler terms, it's the length of one complete cycle of the wave.

For instance, in the exercise where one wave has twice the frequency of another, we could say that the wave with the higher frequency would typically have a shorter wavelength. Why is that? When we increase the frequency, which means more cycles of the wave occur per second, each individual cycle must cover a shorter distance to fit into the same time period.

Visualizing Wavelength

Imagine you are standing at the seashore, watching waves roll in. Each wave's crest is one wavelength apart from the next. If the waves come more frequently, the distance between the crests reduces, just like with waves on a graph. The same principle applies to all types of waves, including sound and light.

Cycles per Second

Another significant wave property is its frequency, which is measured in cycles per second, also known as Hertz (Hz). Essentially, this tells us how many times the wave pattern repeats itself in one second. For students, understanding frequency will help when interpreting data about waves, knowing that a higher frequency means more wave cycles occurring in a given time.

In the context of the exercise provided, drawing one wave with twice the frequency of another simply means that for every single cycle that the first wave completes, the second wave – the one with higher frequency – completes two. Consequently, if the first wave has a frequency of, say, 5 Hz, the second wave would have a frequency of 10 Hz. This is a straightforward way to visually and mathematically grasp the relationship between two waves with different frequencies.

Amplitude

The amplitude of a wave refers to its maximum displacement from its rest position; it's often considered as the 'height' of the wave. In a physical sense, this could mean the height of a sea wave or the volume of a sound wave. It is an indicator of the wave's energy: a high amplitude wave carries more energy. When we illustrate waves graphically, amplitude is shown by the vertical distance from the center line (or the equilibrium position) to the peak or trough.

Amplitude in Practice

If you're at a concert and the music seems loud, you're essentially experiencing high amplitude sound waves. Similarly, large ocean waves during a storm exhibit high amplitudes as well. It's important to note that amplitude is not directly related to frequency; a wave can have a high frequency and a low amplitude or vice versa.