Question

Two small boats are $10\text{m}$ apart on a lake. Each boat pops up and down with a period of $4.0\text{sec}$ due to wave motion on the surface of 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 $5.0\text{m/s}$


Clearly, the separation between boats is $\lambda /2=10\Rightarrow \lambda =20\text{m}$ ..... $\left(1\right)$
The time period of oscillation of each boat $T=4\text{sec}$ ..... $\left(2\right)$
$\therefore$ Linear frequency is $f=\frac{1}{4}\text{Hz}$

For the wave motion,
$v=f\lambda$
$\Rightarrow v=\frac{1}{4}\times 20=5\text{m/s}$

Hence, $\left(B\right)$ is the correct answer.