Question

The data listed below are for mechanical waves. Which wave has the greatest energy? amplitude = 7 cm; wavelength = 12 cm; period = 14 seconds amplitude =12 cm; wavelength = 14 cm; period = 7 seconds amplitude = 14 cm; wavelength = 7 cm; period = 12 seconds

Answer 1

Explanation :

The amplitude, wavelength and time period of three waves are given.

We know that energy of a wave is given by :

$E=\dfrac{h\ c}{\lambda}$

It is clear that energy of a wave is inversely proportional to the wavelength i.e $E\propto \dfrac{1}{\lambda}$

So, the wave having less wavelength will have the greatest energy.

Also, we know that energy of a wave is directly proportional to the square of amplitude i.e. $E\propto(Amplitude)^2$

So, again the wave having maximum amplitude will have maximum energy.

Hence, the correct option is (C) i.e. "amplitude = 14 cm; wavelength = 7 cm; period = 12 seconds".

Answer 2

The equation for the energy of a wave is given by the equation of E = A^2 where E is the energy of the wave and A is the amplitude. The higher the amplitude, the greater the energy of the wave is and vice versa. An amplitude of 14cm has the greatest energy of the wave followed by 12cm and then 7cm.