Question

Two small boats are 10 m 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

The correct option is B $5.0m/s$

Distance between boats must be ha;f of wavelength because question says that when one boat is at a highest point the other is at lowest point and both boats are always within a single cycle of the wave.

Hence wavelength$=2\times$ distance between the boats$=(2\times 10)m=20m$

Frequency$=\frac{1}{Timeperiod}=\frac{1}{4}Hz$

Now speed of the wave $=$ wavelength of wave$\times$ frequency of wave $=20\times \frac{1}{4}=5m/s$

Hence speed of wave $=5m/s$