Question

Which statement is true?

A.Waves with the longest wavelengths have the most energy.
B.Waves with the highest frequencies have the longest wavelengths.
C.Waves with the shortest wavelengths have the lowest frequencies.
D.Waves with the longest wavelengths have the lowest frequencies.

Answer 1

The correct statement is D: Waves with the longest wavelengths have the lowest frequencies. This is based on the principles of wave behavior where longer wavelengths correlate with lower energy and lower frequencies.

Step-by-step explanation:

The question pertains to understanding the relationship between wavelength, frequency, and energy of waves. Given the principles of wave behavior, especially in the context of electromagnetic radiation, we can assess the statements provided to find the one that is true.

Let's examine each statement:

• A. Waves with the longest wavelengths have the most energy. This statement is false because, according to the principles of wave behavior, waves with longer wavelengths have less energy.
• B. Waves with the highest frequencies have the longest wavelengths. This statement is false because high frequency correlates with shorter wavelengths, not longer.
• C. Waves with the shortest wavelengths have the lowest frequencies. This is false as shorter wavelengths are associated with higher frequencies.
• D. Waves with the longest wavelengths have the lowest frequencies. This statement is true. In the context of electromagnetic waves, those with longer wavelengths do indeed have lower frequencies.

Therefore, the correct answer is D: Waves with the longest wavelengths have the lowest frequencies.

Answer 2

The correct statement is D. Waves with the longest wavelengths have the lowest frequencies.

Wavelength and frequency are two important characteristics of waves. Wavelength is the distance between two corresponding points on a wave, such as two crests or two troughs. Frequency, on the other hand, is the number of waves that pass a given point in one second. The unit of frequency is Hertz (Hz).

The relationship between wavelength and frequency is inverse. This means that when the wavelength is longer, the frequency is lower. When the wavelength is shorter, the frequency is higher. This relationship can be expressed mathematically as:

frequency = wave speed / wavelength

Since the speed of a wave is constant in a given medium if the wavelength is longer, the frequency must be lower, and vice versa.

Energy, on the other hand, is related to the amplitude of a wave, which is the height of the wave's crest or depth of its trough. The higher the amplitude, the more energy a wave carries. The relationship between energy and wavelength is not as straightforward as the relationship between wavelength and frequency. The energy of a wave is related to both its amplitude and frequency, and can be calculated using the following equation:

energy = Planck's constant x frequency

Therefore, the statement "waves with the longest wavelengths have the most energy" is incorrect. The energy of a wave depends on both its amplitude and frequency, not just its wavelength.