Wave Frequency Calculation: Period Of 1/3 Second
Hey everyone! Let's dive into a cool physics problem today that deals with waves and their frequencies. We're going to figure out the frequency of a wave when we know its period. It's a pretty straightforward calculation, and once you get the hang of it, you'll be solving these in no time. So, let's jump right in!
Understanding Wave Period and Frequency
First, let's define our terms, guys. The period of a wave is the time it takes for one complete cycle of the wave to pass a certain point. Think of it like this: if you're watching a buoy bobbing up and down in the water, the period is the time it takes for the buoy to go from its highest point, down to its lowest point, and back up to its highest point again. It’s usually measured in seconds.
Now, frequency is the number of complete wave cycles that pass a point in one second. So, if our buoy bobs up and down three times in one second, the frequency of the wave is 3 cycles per second. We measure frequency in Hertz (Hz), where 1 Hz means one cycle per second. The relationship between period and frequency is key to solving our problem. They are inversely related, meaning that if the period increases, the frequency decreases, and vice versa. This makes sense if you think about it: if it takes a long time for one cycle to complete (long period), then fewer cycles will occur in one second (low frequency).
The formula that connects these two is super simple and fundamental in wave physics. It's expressed as:
Frequency (f) = 1 / Period (T)
Where:
fis the frequency in Hertz (Hz)Tis the period in seconds (s)
This formula is your best friend when dealing with wave problems, so make sure you memorize it! It tells us that to find the frequency, all we need to do is take the reciprocal of the period. This inverse relationship is crucial for understanding how waves behave and is a cornerstone concept in physics. Understanding this relationship allows us to easily convert between period and frequency, making it simple to analyze wave behavior in various contexts. Think about different types of waves, from sound waves to light waves; this principle applies universally.
Solving the Problem: Period of 1/3 Second
Okay, now that we've got our definitions and formula down, let's tackle the question. We're given that the wave has a period of 1/3 second. That means it takes 1/3 of a second for one complete wave cycle to occur. Our goal is to find out how many of these cycles happen in one full second, which will give us the frequency.
Using our formula, f = 1 / T, we can plug in the given period:
f = 1 / (1/3)
To divide by a fraction, we simply multiply by its reciprocal. The reciprocal of 1/3 is 3/1, which is just 3. So, our equation becomes:
f = 1 * 3
f = 3 Hz
So, a wave with a period of 1/3 second has a frequency of 3 Hz. This means that three complete wave cycles occur every second. It's as simple as that! This result highlights the direct application of the formula and the inverse relationship between period and frequency. By understanding this concept, we can quickly calculate wave characteristics in various scenarios, whether it's analyzing sound waves in music or electromagnetic waves in communication systems. The beauty of physics lies in these simple yet powerful relationships that govern the natural world.
Why the Other Options Are Incorrect
It's also helpful to understand why the other answer choices are wrong. This can reinforce our understanding of the concept and help us avoid common mistakes in the future. Let's take a look at the options:
- A) 33 Hz: This is incorrect. It seems like this might be a result of some miscalculation or misunderstanding of the formula. There's no clear way to arrive at 33 Hz from the given period of 1/3 second using the correct formula.
- B) 67 Hz: This is also incorrect. Again, there's no direct or logical way to obtain 67 Hz when the period is 1/3 second. It's important to always double-check your calculations and ensure you're applying the correct formula.
- D) 300 Hz: This option is significantly higher than our correct answer, suggesting a more drastic error in calculation. It might come from incorrectly inverting the period or multiplying instead of dividing. Always remember the inverse relationship and the correct application of the formula.
By understanding why these options are wrong, we solidify our understanding of why 3 Hz is the correct answer. It reinforces the importance of accurate calculations and a clear grasp of the fundamental relationship between period and frequency.
Real-World Applications of Wave Frequency
Understanding wave frequency isn't just about solving textbook problems; it has tons of real-world applications! Frequency is a crucial concept in many areas of science and technology. Let's explore a few examples:
- Sound: The frequency of a sound wave determines its pitch. High-frequency sound waves sound high-pitched (like a whistle), while low-frequency sound waves sound low-pitched (like a bass drum). Musicians and audio engineers work with frequencies all the time to create the sounds we hear and enjoy.
- Electromagnetic Waves: Light, radio waves, microwaves, and X-rays are all types of electromagnetic waves, and they each have different frequencies. The frequency of an electromagnetic wave determines its properties and how it interacts with matter. For example, the frequency of radio waves is used to tune into different radio stations, and the frequency of light determines its color.
- Medical Imaging: Medical imaging techniques like MRI and ultrasound use waves with specific frequencies to create images of the inside of the human body. Understanding frequency is essential for interpreting these images and diagnosing medical conditions.
- Telecommunications: The frequencies of electromagnetic waves are used to transmit information in telecommunications systems, such as cell phones and Wi-Fi. Different frequencies are allocated to different uses to prevent interference and ensure efficient communication.
These are just a few examples, but they illustrate how important understanding wave frequency is in our daily lives. From the music we listen to, to the medical treatments we receive, to the technology we use to communicate, frequency plays a vital role. Understanding the fundamentals allows us to appreciate the complex and interconnected world around us.
Conclusion
So, to recap, the frequency of a wave with a period of 1/3 second is 3 Hz. We figured this out by using the formula f = 1 / T, which shows the inverse relationship between frequency and period. Remember this formula, and you'll be able to solve all sorts of wave problems! More importantly, understanding the relationship between period and frequency gives you a powerful tool for analyzing and understanding the world around you.
I hope this explanation was helpful, guys! If you have any more questions about waves or physics, feel free to ask. Keep exploring and keep learning! Physics is all about understanding how the world works, and waves are just one piece of the puzzle. By mastering these fundamental concepts, you'll be well on your way to unlocking the mysteries of the universe. Happy wave-ing!
