Calculating Minimum Distance Between Phase Shifted Points in Water

Are you scratching your head over how to compute the minimum distance between two points in water that are π/3 radians out of phase at a frequency of 2500 Hz? You’re not alone! Let's break it down into bite-sized pieces and make it both fun and understandable.

First off, let’s get clear on what we’re faced with here. Essentially, you need to know about waves, their properties, and the relationship between speed, frequency, and wavelength. Sounds daunting? Don’t worry; I’ve got you covered!

So, here’s the thing: The speed of sound in water is about 1500 m/s. That means when a sound wave travels through water, it does so fairly quickly. We’ve got this nifty equation that ties together speed (v), frequency (f), and wavelength (λ):
[ v = f \cdot \lambda ]

Rearranging this gives us a way to find wavelength:
[ \lambda = \frac{v}{f} ]

Plugging in our numbers:
[ \lambda = \frac{1500 , \text{m/s}}{2500 , \text{Hz}} = 0.6 , \text{m} ]

So, the wavelength of our wave in water is 0.6 meters. Easy enough, right? But what if I told you that the fun has just begun? We’re now on a mission to figure out how two points can be out of phase by π/3 radians.

Now, here comes the interesting part! To find that minimum distance, we need a little relationship involving our newfound wavelength. The relationship looks like this:
[ \text{Phase Difference} = \frac{2\pi}{\lambda} \cdot d ]

In this case, our phase difference is π/3 radians, so let’s set the equation up:
[ \frac{2\pi}{0.6} \cdot d = \frac{\pi}{3} ]

This equation looks a bit intimidating at first glance, doesn’t it? But hang tight. Simplifying this gives us:
[ d = \frac{\pi/3}{2\pi/0.6} ]

Canceling out π leaves us with:
[ d = \frac{0.6}{6} = 0.1 , \text{m} ]

Yep, that’s right! The minimum distance between two points in water that are π/3 radians out of phase at a frequency of 2500 Hz is 0.1 meters—which leads us to option B in our original question.

So, why spend so much time on this? Well, understanding wave behavior lays the foundation for grasping more complex topics in physics. Whether it’s sound, light, or other forms of energy transfer, these key principles will guide you through the world of waves to more advanced concepts. And who doesn’t want to master those A Level physics exams?

Take a moment to reflect on how fascinating waves can be—everything from a quiet ripple on a pond to a resounding clap of thunder involves these principles. It’s not just about numbers and equations; it’s about understanding the world around you. Want to further hone your skills? Keep practicing and experimenting with more problems like this, and soon you’ll feel like a physics pro!

There you have it, folks! Physics made simple. Now, take these insights and go tackle those exam questions with confidence—you’ve got this!