Elaborate on the difference between the energy of the two waves seen here
A. Wave A has more energy than Wave B because the wavelength of Wave A is greater
B. Wave B has more energy: the amplitude of Wave B is double that of Wave A.
C. Wave energy is directly proportional to frequency and wavelength, therefore Wave A has more energy.
D.Wave B has more energy than Wave A because the frequency of Wave B is greater
The correct answer is B. Wave B has more energy: the amplitude of Wave B is double that of Wave A.
The energy of a wave is determined by its amplitude, not its wavelength or frequency. Amplitude refers to the maximum displacement of particles in a medium from their rest position. In other words, it measures the height or intensity of the wave.
Wave A may have a greater wavelength, meaning it takes longer for one complete cycle of the wave to pass by a point. However, the wavelength does not directly determine the energy of the wave. Similarly, the frequency of a wave refers to the number of cycles that occur in a given time period. While a higher frequency wave may appear to have more energy due to its rapid oscillation, frequency alone does not determine the energy of a wave.
In the given scenario, it is explicitly stated that the amplitude of Wave B is double that of Wave A. Since amplitude is directly related to the energy of a wave, Wave B has more energy compared to Wave A.
Out of the given options, the correct answer is B. Wave B has more energy because the amplitude of Wave B is double that of Wave A. Let's discuss the difference between the energy of these two waves in detail.
1. Option A states that Wave A has more energy than Wave B because the wavelength of Wave A is greater. However, the wavelength of a wave does not directly affect its energy. The wavelength is a measure of the distance between two consecutive corresponding points on a wave, such as two peaks or two troughs. It is unrelated to the energy carried by the wave.
2. Option B correctly states that Wave B has more energy because the amplitude of Wave B is double that of Wave A. The amplitude of a wave represents the maximum displacement or height of a wave from its equilibrium position. In terms of energy, the larger the amplitude, the more energy is carried by the wave. Therefore, Wave B having a higher amplitude means it carries more energy than Wave A.
3. Option C mentions that wave energy is directly proportional to frequency and wavelength, and therefore, Wave A has more energy. However, this is incorrect. While it is true that wave energy is related to frequency and wavelength, it is not solely determined by either of them individually. The energy of a wave depends on both its amplitude and frequency, not just its wavelength.
4. Option D suggests that Wave B has more energy than Wave A because the frequency of Wave B is greater. However, frequency alone does not determine the energy of a wave. Frequency indicates the number of complete wave cycles passing a given point per unit of time. While it can affect other characteristics of a wave, such as its pitch, it is not the primary determinant of its energy.
In summary, the correct answer is B. Wave B has more energy because its amplitude is double that of Wave A.