Question

select the statement(s) that accurately describe the relationship between the energy of a wave and the frequency and wavelength. the more energy a wave has, the lower the frequency will be. the more energy a wave has, the higher the frequency will be. the more energy a wave has, the longer the wavelength will be. the more energy a wave has, the longer the wavelength and lower the frequency will be. the more energy a wave has, the shorter the wavelength will be.

Explanation:

To solve this, we use the relationships \( E = h
u \) (where \( E \) is energy, \( h \) is Planck's constant, \(
u \) is frequency) and \( c=\lambda
u \) (where \( c \) is speed of light, \( \lambda \) is wavelength). From \( E = h
u \), energy (\( E \)) is directly proportional to frequency (\(
u \))—so higher energy means higher frequency. From \( c=\lambda
u \), frequency and wavelength are inversely proportional (\(
u=\frac{c}{\lambda} \)). Since \( E \propto
u \) and \(
u \propto \frac{1}{\lambda} \), higher energy means shorter wavelength (because higher frequency implies shorter wavelength, as \( \lambda=\frac{c}{
u} \)).

• "The more energy a wave has, the lower the frequency will be" is wrong (energy and frequency are directly proportional).
• "The more energy a wave has, the higher the frequency will be" is correct (from \( E = h

u \)).

• "The more energy a wave has, the longer the wavelength will be" is wrong (energy and wavelength are inversely related).
• "The more energy a wave has, the longer the wavelength and lower the frequency will be" is wrong (contradicts direct energy - frequency and inverse frequency - wavelength relationships).
• "The more energy a wave has, the shorter the wavelength will be" is correct (since \( E \propto

u \) and \(
u \propto \frac{1}{\lambda} \), so \( E \propto \frac{1}{\lambda} \), higher \( E \) means shorter \( \lambda \)).

Answer:

B. The more energy a wave has, the higher the frequency will be, E. The more energy a wave has, the shorter the wavelength will be