Question

the energy of wave 1 is double the energy of wave 2. what can you infer about the wave properties of wave 1 compared to the wave properties of wave 2? a the frequency of both waves must be the same. b the frequency of wave 1 is half the frequency of wave 2. c the wavelength of wave 1 is double the wavelength of wave 2. d the wavelength of wave 1 is half the wavelength of wave 2.

Explanation:

Step1: Recall energy - frequency relation

The energy of a wave is given by $E = hf$, where $E$ is energy, $h$ is Planck's constant and $f$ is frequency. If the energy of Wave 1 ($E_1$) is double the energy of Wave 2 ($E_2$), i.e., $E_1 = 2E_2$. Then $h f_1=2hf_2$, so $f_1 = 2f_2$.

Step2: Recall frequency - wavelength relation

The speed of a wave $v=\lambda f$. Assuming the speed of both waves is the same (in the same medium). If $f_1 = 2f_2$, then from $v=\lambda f$ we have $\lambda_1f_1=\lambda_2f_2$. Substituting $f_1 = 2f_2$ gives $\lambda_1\times2f_2=\lambda_2f_2$, so $\lambda_1=\frac{1}{2}\lambda_2$.

Answer:

D. The wavelength of Wave 1 is half the wavelength of Wave 2