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

Answer : The correct option is, amplitude = 14 cm; wavelength = 7 cm; period = 12 seconds

Explanation :

The amplitude, wavelength and time period of three types of waves.

As we know that energy of a wave is given as :

$E=\frac{h\times c}{\lambda}$

From this we conclude that the energy of a wave is inversely proportional to the wavelength.

i.e $E\propto \frac{1}{\lambda}$

As the the wavelength increases, the energy will decreases and vice-versa.

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

Also, there is a relation between the energy and the amplitude wave. That is the energy of a wave is directly proportional to the square of amplitude.

i.e. $E\propto(Amplitude)^2$

That means the wave have maximum amplitude will have maximum energy.

Hence, the correct option is, amplitude = 14 cm; wavelength = 7 cm; period = 12 seconds.

Answer 2

The relationship between energy and wavelength is shown by:
E = hc/wavelength
As we can see, there is an inverse relation between energy and the wavelength. The greater the energy, the shorter the wavelength. Among the mechanical waves listed, at the wavelength of 7 cm.