A floating leaf bobs up and down two complete cycles each second as water waves pass by at
a speed of $10 \mathrm {~m} / \mathrm { s }$ .How far apart are the waves?
A) 1 meter
B) 2 meters
C) 5 meters
D) 20 meters

Question

A floating leaf bobs up and down two complete cycles each second as water waves pass by at
a speed of $10 \mathrm {~m} / \mathrm { s }$ .How far apart are the waves? 
A) 1 meter
B) 2 meters
C) 5 meters
D) 20 meters

Quizplus · Accepted Answer

To find out how far apart the waves are, we need to determine the wavelength of the water waves. The wavelength ($\lambda$) is the distance between two consecutive crests or troughs of a wave. We can calculate the wavelength using the wave speed ($v$) and the frequency ($f$) of the waves with the formula:
$$
\lambda = \frac{v}{f}
$$
Given that the leaf bobs up and down two complete cycles each second, the frequency of the water waves is $2 \mathrm {~Hz}$ (since one cycle per second is one hertz).
The wave speed is given as $10 \mathrm {~m/s}$.
Now we can plug these values into the formula:
$$
\lambda = \frac{10 \mathrm {~m/s}}{2 \mathrm {~Hz}} = \frac{10 \mathrm {~m/s}}{2 \mathrm {~s^{-1}}} = 5 \mathrm {~m}
$$
Therefore, the waves are 5 meters apart.
The correct answer is c. 5 meters.

A Floating Leaf Bobs Up and Down Two Complete Cycles 10 m/s10 \mathrm {~m} / \mathrm { s }10 m/s

A Floating Leaf Bobs Up and Down Two Complete Cycles $10 \mathrm {~m} / \mathrm { s }$