Questions: A wooden float at the end of a fishing line makes eight complete oscillations in 10 s . If it takes 3.60 s for a single wave to travel 11 m , what is the wavelength of the water waves? (A) 4.82 m (B) 5.82 m (C) 3.82 m

Solution Steps

The float makes 8 complete oscillations in 10 seconds. The frequency \( f \) is given by the number of oscillations per second.

\[ f = \frac{8 \text{ oscillations}}{10 \text{ s}} = 0.8 \text{ Hz} \]

The time it takes for a single wave to travel 11 meters is 3.60 seconds. The wave speed \( v \) can be calculated using the formula:

\[ v = \frac{\text{distance}}{\text{time}} = \frac{11 \text{ m}}{3.60 \text{ s}} = 3.0556 \text{ m/s} \]

The wavelength \( \lambda \) can be found using the wave speed \( v \) and the frequency \( f \) with the formula:

\[ \lambda = \frac{v}{f} = \frac{3.0556 \text{ m/s}}{0.8 \text{ Hz}} = 3.8195 \text{ m} \]

Final Answer