Breaking Down Wave Frequency: Why It Matters

A wave moves through its medium at 20 m/s with a wavelength of 4 m. What is the frequency of the wave?

• A. 24 s−1
• B. 5 s−1
• C. 16 s−1
• D. 80 s−1

Answer: (B)

To determine the frequency of a wave, you can use the relationship between wave speed (v), wavelength (λ), and frequency (f), which is expressed by the equation: \[ v = f \times λ \] In this particular scenario, the wave speed is given as 20 m/s, and the wavelength is 4 m. To find the frequency, you can rearrange the equation to solve for frequency: \[ f = \frac{v}{λ} \] Substituting the known values into the equation: \[ f = \frac{20 \text{ m/s}}{4 \text{ m}} \] Calculating this gives: \[ f = 5 \text{ s}^{-1} \] This calculation shows that the frequency of the wave is 5 Hz, which means the correct answer is indeed 5 s⁻¹. The frequency indicates how many wave cycles pass a point in one second, and in this case, it's 5 cycles per second.

Have you ever stood on a beach, mesmerized by the rhythm of the waves? There's something almost hypnotic about it. But what if I told you that there’s a science behind those waves? Today, we're diving into a simple but crucial concept: wave frequency. Don’t worry! It’ll be easy-peasy.

So, picture this: A wave is zipping through the medium at a snappy 20 meters per second with a wavelength of 4 meters. Now, a question pops up—what’s the frequency of this wave? It’s like asking how many times those ocean waves crash against the shore in a minute. Sounds cool, right?

Let’s break it down! To calculate the frequency (symbolized as (f)), we need to rely on a handy little formula that connects wave speed ((v)), frequency, and wavelength ((λ)). The formula looks like this:

[ v = f \times λ ]

Here’s the scoop: wave speed tells us how fast the wave travels, while wavelength is the distance from one wave crest to the next. Now, if you rearrange the formula, you can isolate frequency:

[ f = \frac{v}{λ} ]

Getting to the nitty-gritty, we can plug in our values:

• Wave speed (v) = 20 m/s

• Wavelength (λ) = 4 m

Now, let’s do the math:

[ f = \frac{20 \text{ m/s}}{4 \text{ m}} = 5 \text{ s}^{-1} ]

Bingo! The frequency (that’s how many waves pass a point each second) is 5 Hertz (Hz). Think of it this way: if you blink five times a second, you've got a good rhythm!

Isn’t that neat? But why should you care about frequency? If you’re eyeing a career in nursing or any health-related field, understanding waves—especially sound and light waves—can give you a better grasp of how diagnostics, treatments, and therapies work. For example, sonar in ultrasound or heartbeats captured by an EKG, all rely on wave properties!

Now, you might be wondering, “Why do we need to know about frequency in the first place?” Well, the frequency indicates how often something occurs in a certain timeframe. In the realm of waves, this could mean anything from sound waves that help us hear to the radio waves that power our communication devices.

But hold on—what about differences in waves? Sound waves and light waves might differ in how they interact with their environments, but the basic principles maintain their relevance. When you're in the thick of understanding these concepts for an exam, remember that grasping the fundamentals will make everything easier.

In summary, grasping the connection between wave speed, wavelength, and frequency can feel like assembling building blocks—it’s all about finding the right fit. So, the next time you see waves or hear about them in class, you'll know that there's rhythm nestled behind the science. Wave frequency isn’t just a number; it’s a whole world of understanding waiting to unfold!

And there you have it! The importance of frequency, made simple. Ready to ride the waves of knowledge?