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Answer the question (use latex) and tell if it comes under "number and operations" or "algebra and functions" or "calculus"

To solve this problem, let's go through each part:

### Given Data:
- Wave speed (\( v \)) = 570 m/s
- Wavelength (\( \lambda \)) = 9.8 m

### Part (a): Frequency of the Wave
The formula relating wave speed, wavelength, and frequency is:
\[
v = f \cdot \lambda
\]
Rearrange to solve for frequency (\( f \)):
\[
f = \frac{v}{\lambda}
\]
Substitute the values:
\[
f = \frac{570 \, \text{m/s}}{9.8 \, \text{m}} = 58.16 \, \text{Hz}
\]

So, the frequency of the wave is **58.16 Hz**.

### Part (b): Period of the Wave
The period (\( T \)) is the reciprocal of the frequency:
\[
T = \frac{1}{f}
\]
Substitute the frequency we just calculated:
\[
T = \frac{1}{58.16} \approx 0.0172 \, \text{s}
\]

So, the period of the wave is approximately **0.0172 seconds**.

### Classification of the Problem
This problem falls under the category of **"number and operations"** since it involves basic arithmetic operations with given quantities.

---

Would you like further details or have any questions?

### Related Questions
1. What would happen to the frequency if the wavelength was doubled?
2. How does changing the wave speed affect the period?
3. If a wave's period is known, how can you find its frequency directly?
4. How does wavelength impact the energy of a wave in terms of frequency?
5. What units are typically used for wavelength, frequency, and period?

### Tip
Remember, frequency and period are inversely related, so as one increases, the other decreases.

A wave has a speed of 570 m/s and a wavelength of 9.8 m. What are the (a) frequency and (b) period of the wave?

Learn how to calculate the frequency and period of a wave given its speed (570 m/s) and wavelength (9.8 m). This guide covers essential wave properties and calculations, suitable for high school students in Grades 9-12.

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