Wave Frequency Calculation: Step-by-Step Solution

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Hey guys! Let's break down this physics problem together. We need to find the frequency of a wave traveling on a string. The speed of the wave is given as 400 cm/s, and its wavelength is 1 meter. Ready? Let's dive in!

Understanding the Basics

Before we jump into the calculations, let's make sure we're all on the same page with the key concepts.

  • Frequency (f): This is the number of complete wave cycles that pass a point in one second. We measure it in Hertz (Hz).
  • Wavelength (位): This is the distance between two identical points on consecutive waves, like the distance from one crest to the next. We usually measure it in meters (m) or centimeters (cm).
  • Wave Speed (v): This is how fast the wave is moving through the medium. We measure it in meters per second (m/s) or centimeters per second (cm/s).

These three amigos are related by a simple formula:

v = f位

Where:

  • v = wave speed
  • f = frequency
  • 位 = wavelength

Make sense? Awesome, let's keep going!

Setting Up the Problem

Okay, let's organize what we know:

  • Wave speed, v = 400 cm/s
  • Wavelength, 位 = 1 meter

But wait! We need to make sure our units are consistent. Since the speed is in cm/s and the wavelength is in meters, let's convert the wavelength to centimeters. We know that 1 meter is equal to 100 centimeters, so:

位 = 1 meter = 100 cm

Now we have:

  • v = 400 cm/s
  • 位 = 100 cm

Perfect! Now we can use our formula to find the frequency.

Calculating the Frequency

Remember our formula:

v = f位

We want to find the frequency (f), so let's rearrange the formula to solve for f:

f = v / 位

Now, plug in our values:

f = 400 cm/s / 100 cm

f = 4 Hz

Oops! It seems there was a miscalculation somewhere, or the provided options might be incorrect. Let's double-check our work to ensure accuracy, and if needed, we'll address any discrepancies or provide the correct methodology for solving similar problems. Understanding each step is crucial for confidently tackling wave-related questions! Always verify the units and formulas for accuracy.

It looks like the correct calculation is as follows:

f = 400 cm/s / 100 cm
f = 4 Hz

However, the options provided do not include '4' as a possible answer. Therefore, it might be beneficial to double-check the initial problem statement or context for potential errors. If all the provided information is accurate, we might conclude that none of the provided options are correct, and the actual answer is 4 Hz.

Analyzing the Options

Let's look at the provided options:

a) 40 b) 133 c) 120 d) 20 e) 30

None of these match our calculated frequency of 4 Hz. There might be a typo in the options, or perhaps in the original problem statement. If we had to choose the closest answer, it would depend on the context or any additional information available. However, based purely on our calculations, none of the provided answers are correct.

Potential Sources of Error

Here are a few things that might have gone wrong:

  • Typo in the problem statement: Maybe the wave speed or wavelength was written incorrectly.
  • Typo in the options: Maybe one of the options was supposed to be 4 Hz.
  • Misunderstanding of the problem: We might have misinterpreted something in the problem statement (though we tried to be very careful!).

Without more information, it's hard to say for sure. But our calculations are solid, so we can be confident in our result.

Converting Units to Meters per Second (m/s)

To convert the speed from cm/s to m/s, remember that 1 m = 100 cm. Therefore, to convert cm/s to m/s, divide by 100.

v = 400 cm/s = 400 / 100 m/s = 4 m/s

Now we have:

  • v = 4 m/s
  • 位 = 1 m

Using the formula f = v / 位:

f = 4 m/s / 1 m

f = 4 Hz

Practice Problems

Want to test your understanding? Try these practice problems:

  1. A wave has a speed of 500 cm/s and a wavelength of 2 meters. What is its frequency?
  2. A wave has a frequency of 10 Hz and a wavelength of 0.5 meters. What is its speed?

Work through these, and you'll be a wave-calculating pro in no time!

Why This Matters

Understanding wave frequency isn't just about solving physics problems. It's crucial in many real-world applications:

  • Music: The frequency of a sound wave determines the pitch of a note.
  • Telecommunications: Radio waves and microwaves use frequency to transmit information.
  • Medical Imaging: Ultrasound uses high-frequency sound waves to create images of the inside of the body.

So, the next time you listen to music, use your cell phone, or get an ultrasound, remember that it all relies on understanding wave frequency!

Conclusion

Alright, physics pals, we've tackled this wave frequency problem step by step. Remember to always double-check your units, use the correct formula, and think critically about the problem. Even if the provided options don't match your answer, don't panic! Review your work, and consider potential sources of error. Keep practicing, and you'll master these concepts in no time!