Waves

Let's walk through Worked Example 1, where we calculate the speed of a water wave on Lake Naivasha. First, the given information: the wavelength λ is 0.5 metres – that's the distance between successive crests – and the frequency f is 2 hertz, meaning two wave cycles occur each second. Using the basic wave relation v = f · λ, we multiply the two numbers: 2 × 0.5 equals 1, so the wave speed v is 1 metre per second. What does that tell us? It means the wave travels one metre every second across the surface of the lake – a gentle, steady ripple you could easily observe from the shore. Any questions so far? If anything's unclear, feel free to ask – we'll pause and make sure everyone's comfortable with the calculation.

Class, let's work through Example 2: figuring out the pitch of a traditional drumbeat recorded at 120 beats per minute in a bustling Kenyan market. First, we convert the beats per minute (BPM) to hertz (Hz). Divide 120 bpm by 60 seconds per minute, which gives us 2 Hz. That means the drum is beating twice each second—quite a low‑pitch rhythm. Notice the "2 Hz" result highlighted there; that's our frequency value. Let's talk about amplitude. The market noise is roughly 60 dB, which tells us how loud the surrounding sounds are. Higher decibel (dB) values mean louder sounds, so the drum's loudness will be perceived relative to that background level. Do you see the note that links amplitude to loudness? Think about standing near the drum versus farther away in the market. To recap: we turned 120 bpm into 2 Hz, identified it as a low‑pitch drumbeat, and considered how a 60 dB market background influences the perceived loudness. Any quick questions before we move on?

All right, class, let's work through Example 3, where we identify the color of light with a wavelength of 550 nm and calculate its frequency. First, the slide tells us λ = 550 nanometers, which lies in the visible green region of the spectrum. To find the frequency, we use the relationship f = c / λ, where c is the speed of light (3 × 10⁸ m/s).

Everyone, let's wrap up what we've explored about waves and see how they touch our everyday lives here in Kenya. First, remember the difference between transverse and longitudinal motion: transverse waves move side‑to‑side, like light rippling on water, while longitudinal waves compress and expand, just as sound travels through air. Next, wavelength, frequency, and amplitude are the three partners that determine a wave's speed and energy. Wavelength (the distance between peaks) and frequency (how many peaks pass per second) together set the speed, while a larger amplitude means more energy. Think about sound waves: they let us talk on our phones, listen to music, and even hear the call to prayer across a village. Light waves, on the other hand, power the solar kits we use in remote schools, and they also influence our climate by heating the atmosphere. Looking ahead, our next lesson will dive into wave interference and superposition—how waves can add together or cancel each other out, which is essential for understanding technologies like noise‑cancelling headphones and radio broadcasting.