Question

Two small boats are $10m$ apart on a lake. Each pops up and down with a period of $4.0\text{seconds}$ due to wave motion on the surface of the water. When one boat is at its highest point, the other boat is at its lowest point. Both boats are always within a single cycle of the waves. The speed of the waves is

• A. $2.5\text{m/s}$
• B. $5.0\text{m/s}$
• C. $14\text{m/s}$
• D. $40\text{m/s}$

Answer 1

The correct option is B $5.0\text{m/s}$

$\frac{\lambda }{2}=10\text{m}\Rightarrow \lambda =20\text{m}$

$\text{Time period}=T=4\text{sec}$

$V=\frac{\lambda }{T}=\frac{20}{4}=5\text{m/s}$