8. If you tap your finger in a pool of water twice every second, what is the frequency of the waves you are generating? 9. If the same waves from problem 8 travel away from your finger at a speed of \( 1 \mathrm{~m} / \mathrm{s} \), what is their wavelen g.

Let's solve the problems step by step. ### Problem 8: Frequency of the Waves 1. **Known Condition**: You tap your finger twice every second. 2. **Definition of Frequency**: Frequency (\( f \)) is defined as the number of cycles (or taps, in this case) per unit time (in seconds). Since you tap your finger twice every second, the frequency can be calculated as: \[ f = \frac{\text{Number of taps}}{\text{Time in seconds}} = \frac{2 \text{ taps}}{1 \text{ second}} = 2 \text{ Hz} \] ### Problem 9: Wavelength of the Waves 1. **Known Conditions**: - Frequency (\( f \)) from Problem 8 is \( 2 \text{ Hz} \). - Speed of the waves (\( v \)) is \( 1 \text{ m/s} \). 2. **Relationship Between Speed, Frequency, and Wavelength**: The relationship is given by the formula: \[ v = f \cdot \lambda \] where \( \lambda \) is the wavelength. 3. **Rearranging the Formula to Find Wavelength**: \[ \lambda = \frac{v}{f} \] 4. **Substituting the Known Values**: \[ \lambda = \frac{1 \text{ m/s}}{2 \text{ Hz}} = 0.5 \text{ m} \] ### Final Answers: - The frequency of the waves is \( 2 \text{ Hz} \). - The wavelength of the waves is \( 0.5 \text{ m} \).