Understanding the Speed of Sound: How Frequency and Wavelength Play a Role

When it comes to understanding sound, it’s not all about how loud or soft something is. It's also about how fast those waves travel, which brings us to an exciting topic: the speed of sound! You might be asking yourself: how do we figure that out? Well, let's break it down step by step, focusing on a particular example that ties into the PSC1121 curriculum at UCF.

So, imagine you hear a voice producing a sound with a frequency of 110 Hz and a wavelength of 3.14 m. What’s the speed of sound in this case? Is it 300 m/sec? Maybe 480 m/sec? Or is it something else entirely? The correct answer is actually 345.4 m/sec. How do we get there? Great question!

We can use the relationship laid out in a nifty formula:

[ v = f \times \lambda ]

Where:

• ( v ) is the speed of sound,
• ( f ) is the frequency (that’s the 110 Hz we’ve got), and
• ( \lambda ) is the wavelength (3.14 m in this example).

Here’s the thing: when we plug in these numbers:

[ v = 110 , \text{Hz} \times 3.14 , \text{m} ]

You get:

[ v = 345.4 , \text{m/sec} ]

This is a fantastic demonstration of how frequency and wavelength interact, creating pathways for sound to travel through our air. In typical conditions—say at room temperature—sound travels at about 343 m/sec. So, our calculated speed fits perfectly within what you'd expect!

You might wonder, how do the other options stack up? Well, the values of 300 m/sec, 480 m/sec, and 235 m/sec fall outside the expected range for sound traveling through air, and these could imply either different media (like water or steel) or simply mistakes in calculation.

Understanding this relationship is critical, not just for exam purposes but for grasping how sound waves function in our world. Think about everyday experiences: when you're at a concert, the sound doesn’t just pop into existence; it travels through the air to reach your ears. Sound is more than vibrations; it’s a symphony of physics at work!

So next time you're studying for that exam, remember, you’re not just memorizing numbers and equations — you are learning about the fundamental principles that govern how we experience sound in our lives. Keep these concepts close to your heart (and your study notes), and you’ll have a much easier time tackling the questions that come your way!