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.