Problem 18Q

Two linear waves have the same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what factor?

Solution 18Q

Two linear waves have the same amplitude and are identical except the wavelength of one is half the other. The thing to keep in mind is that the Energy of the wave is proportional to the square of the frequency. As wavelength is inversely proportional to frequency the Energy of the wave is inversely proportional to square of the wavelength.

The energy of the wave,

But we know

The energy of the

Energy of the

Therefore, the 2nd wave with wavelength half that of the 1st wave transmits 4 tunes more energy.