Wave Propagation: Speed & Period Explained

Hey guys! Let's dive into the fascinating world of waves and figure out how to calculate their speed and period. We'll be looking at a specific example involving a square wave, and then we'll explore another scenario with a different frequency. Ready to get started? Let's go!

Calculating Wave Speed for a Square Wave

So, imagine we've got a square wave, like the one described in the problem. We're given some key pieces of information: the distance between points A and B on the wave is 2.9 nm (nanometers), and the oscillation frequency is 390 THz (terahertz). Our mission? To calculate the wave's propagation speed in km/s (kilometers per second). This is a classic physics problem, and the concept of how waves move is fundamental to understanding many phenomena around us, from light to sound.

First things first, what exactly is a wave's propagation speed? Simply put, it's how fast the wave travels through a medium. Think of it like this: if you throw a pebble into a still pond, the ripples (waves) spread out. The speed at which those ripples expand is the propagation speed. The square wave in our example is no different; it's just a different type of wave, and we want to know how quickly it's moving.

The key to solving this lies in a fundamental formula in physics: v = λ * f. Where:

• v represents the wave's speed (what we want to find).
• λ (lambda) represents the wavelength (the distance between two corresponding points on the wave – like from A to B).
• f represents the frequency (how many cycles of the wave pass a point per second). Let's take a closer look at these variables and how to plug in the numbers to arrive at our answer. Remember, always double-check your units!

We already know the frequency (f) is 390 THz. But what about the wavelength (λ)? The problem tells us the distance between A and B is 2.9 nm. In a square wave, the distance between A and B actually represents half of the wavelength. To find the full wavelength we need to understand the relationship between the wavelength and the specific points given in the problem. The distance provided is between two specific points and, therefore, we need to consider how the wavelength is related to these points. This can be visualized or calculated based on the shape of the wave. The square wave has a distinct repeating pattern that makes up a full wavelength, which is why we must take into consideration where the points A and B are located to find the actual wavelength. Consequently, the actual wavelength is double the distance, making it 5.8 nm. A useful tip to solving such a problem is to always analyze the geometry provided in the question!

Now, let's plug those values into our formula. But wait! We need to make sure our units are compatible. We want the final answer in km/s, but our wavelength is in nanometers and our frequency is in terahertz. Let's convert them:

• Wavelength (λ): 5.8 nm = 5.8 x 10^-9 m. Then converting to km: 5.8 x 10^-9 m * (1 km / 1000 m) = 5.8 x 10^-12 km.
• Frequency (f): 390 THz = 390 x 10^12 Hz (Hertz). Because 1 THz is equal to 10^12 Hz.

Now we substitute the values into our formula v = λ * f: v = (5.8 x 10^-12 km) * (390 x 10^12 Hz). The calculation results in v = 2262 km/s. Therefore, the propagation speed of the square wave is approximately 2262 km/s! This shows just how quickly these waves can travel.

Calculating the Period of a Wave

Next, let's consider another scenario. This time, we're given the frequency of a wave: 93 MHz (megahertz). The goal is to determine the period of the wave. The period of a wave is the time it takes for one complete cycle to occur. Think of it as the time it takes for the wave to go through one full oscillation – from crest to trough and back to crest.

The relationship between frequency and period is very simple. They are inversely proportional. This means that as the frequency increases, the period decreases, and vice versa. The formula that connects them is: T = 1 / f. Where:

• T represents the period (measured in seconds).
• f represents the frequency (measured in Hertz).

In our case, the frequency is 93 MHz. So, let's convert it to Hz first: 93 MHz = 93 x 10^6 Hz. Then, substitute it into the formula: T = 1 / (93 x 10^6 Hz). The calculation yields a period of approximately 1.075 x 10^-8 seconds, or 10.75 nanoseconds. This tells us that each cycle of this wave takes a very short amount of time to complete. It is important to know how to calculate the period since it helps us understand the timing of the wave! This can be used in different applications such as signal processing and communications systems.

In summary, both examples illustrate the fundamental concepts of wave propagation. We've seen how to calculate the speed of a wave, considering wavelength and frequency, and how to determine the period based on its frequency. These concepts are very fundamental, guys, and are crucial in understanding the behaviour of waves.

Wavelength, Frequency, and Period: The Building Blocks of Wave Behavior

Waves are all around us. From the light that allows us to see to the sound we hear, waves are essential to our lives. Understanding the relationship between a wave's wavelength, frequency, and period is essential to understanding how they work. These are the three main properties that define a wave and how it behaves. Let's break down each one and then talk about how they relate to each other. You'll find that these concepts are at the very heart of numerous areas of physics and engineering, including optics, acoustics, and telecommunications.

• Wavelength (λ): This is the distance between two corresponding points on a wave, such as two crests (the highest points) or two troughs (the lowest points). Wavelength is measured in units of distance, such as meters (m) or nanometers (nm). For example, the wavelength of visible light determines its color, with shorter wavelengths corresponding to blue and violet light, and longer wavelengths corresponding to red light. It's important to remember that the wavelength of a wave depends on the medium it's traveling through; so, the same wave might have a different wavelength in air compared to in water.

• Frequency (f): This is the number of wave cycles that pass a given point in one second. It's measured in Hertz (Hz), where 1 Hz means one cycle per second. Frequency is directly related to the energy of a wave; higher-frequency waves have higher energy. The frequency of a wave dictates its