Understanding Wave Characteristics: How Frequency Relates to Wavelength

What is the time taken for a wave with a frequency of 780Hz to move one wavelength?

• A. 1/780 s
• B. 780 s
• C. 1.28 ms
• D. 0.00128 s

Answer: (A)

To determine the time taken for a wave with a frequency of 780 Hz to move one wavelength, we start by utilizing the relationship between frequency, wavelength, and period of a wave. The frequency of a wave, which is given in hertz (Hz), tells us how many cycles of the wave pass a given point per second. The period of the wave, on the other hand, is the time it takes for one full cycle to complete. The relationship between frequency (f) and period (T) can be expressed by the formula: \[ T = \frac{1}{f} \] In this case, the frequency is 780 Hz. By substituting this value into the equation, we find: \[ T = \frac{1}{780} \, \text{s} \] Calculating this gives: \[ T \approx 0.00128 \, \text{s} = 1.28 \, \text{ms} \] This means it takes approximately 1.28 milliseconds for one complete cycle (or one wavelength) to occur. Considering the time for one wavelength corresponds to the period of the wave, this supports the correct interpretation that one wavelength takes the same amount of time as its period

Ever wondered how long it takes for a wave to travel one wavelength? You’re not alone! Understanding wave mechanics can be tricky, but once you get the hang of it, you’ll realize it’s not as complicated as it seems. Let's break it down using a wave frequency example of 780 Hz.

First off, it’s important to grasp that frequency, measured in hertz (Hz), tells you how many cycles of a wave pass a point every single second. Cool, right? Now, the time it takes for one complete cycle of a wave to occur is called the period. In simpler terms, the period represents how long it takes the wave to hit the reset button and start over.

Here’s where the magic happens: the relationship between frequency (f) and period (T) can be described with a nifty little formula:

[ T = \frac{1}{f} ]

For our example, that means:

[ T = \frac{1}{780} , \text{s} ]

Take a moment to soak that in! By plugging in our frequency of 780 Hz into the formula, we’re left with:

[ T \approx 0.00128 , \text{s} \text{ or } 1.28 , \text{ms} ]

This means for our wave with a frequency of 780 Hz, it takes about 1.28 milliseconds to complete one full cycle, or in layman’s terms, to travel one wavelength. It’s astounding how we can pin down the timeline of such a dynamic phenomenon, isn’t it?

You might be thinking, "What's the big deal with timing?" Well, imagine listening to your favorite song. The beats and rhythms form waves that travel through the air to your ears. If you can imagine how those waves flow and the timing involved, you can really appreciate the beauty of sound and how successfully we can study them with physics principles.

Understanding the connection here means you can also tackle other wave-related concepts — like amplitude, speed, and even energy transmission. Who knew that the wave equation could lead you down a path of discovery in the world of sound, light, and even water waves?

In exams, it’s super useful to remember these basics and how they intertwine with each other. If you can recall that waves are not only theoretical constructs but practical realities in the world we live in, you’ll definitely be ahead in your A Level Physics studies.

So, sketch this out in your mind: every time a wave moves one wavelength at a frequency of 780 Hz, the clock ticks for 1.28 milliseconds. It’s a great tool in your toolbox when solving any wave-related problems. And who knows? You might even impress your friends with this newfound knowledge!