Question

Two small boats are $10m$ apart on a lake. Each pops up and down with a period of $4.0$ 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. $2.5m/s$
• B. $5.0m/s$
• C. $14m/s$
• D. $40m/s$

Answer 1

Answer: (B)

$5.0m/s$

A time period of the wave $\left(T\right)=4$s

Distance between boats must be half of the wavelength, because question says that one boat is at highest point, the other is at lowest point and both pops up & down with the same period/

$\therefore \lambda =2\times distancebetweenboats$

$2\times 10$=$20m$

Speed of the wave

$=\frac{w}{k}$

$=\frac{\lambda }{T}$

$=\frac{20}{4}$

$=5m/s$

Hence option (B) is correct