In a perfect vacuum, all electromagnetic waves share which common property regardless of their frequency or wavelength?

Introduction / Context:
This question tests your understanding of basic properties of electromagnetic waves in a vacuum. Electromagnetic waves include radio waves, microwaves, infrared, visible light, ultraviolet, X rays and gamma rays. Although they differ greatly in frequency and wavelength, they share some fundamental characteristics. Knowing which property is common to all of them in vacuum is essential for understanding optics, communication technologies and modern physics.

Given Data / Assumptions:

• We are considering electromagnetic waves propagating in a perfect vacuum, not in a material medium like glass or air.
• Examples include radio waves, light and X rays.
• The options suggest equal velocity, wavelength, frequency or all properties being identical.
• We assume standard physics where speed of light in vacuum is a universal constant.

Concept / Approach:
According to Maxwell theory and experimental evidence, all electromagnetic waves travel through vacuum at the same speed, commonly denoted by c, which is approximately 3 * 10^8 metres per second. What distinguishes one type of electromagnetic radiation from another is its frequency and wavelength. These are related by the equation c = lambda * f, where lambda is wavelength and f is frequency. If c is fixed, increasing the frequency must decrease the wavelength, and vice versa. Therefore, while velocity is common to all electromagnetic waves in vacuum, wavelength and frequency vary widely across the spectrum.

Step-by-Step Solution:
Step 1: Recall that electromagnetic waves are self propagating oscillations of electric and magnetic fields and do not require a material medium. Step 2: Recognise that in vacuum, all such waves propagate at the universal speed c, approximately 3 * 10^8 metres per second. Step 3: Remember the relation c = lambda * f. Since c is constant in vacuum, lambda and f must vary inversely to each other. Step 4: Compare radio waves and X rays. They obviously have different wavelengths and frequencies but both travel at the same speed in space. Step 5: Conclude that the only common property among all electromagnetic waves in vacuum is their velocity, not wavelength or frequency.

Verification / Alternative check:
A practical check comes from astronomy and satellite communication. Signals from radio telescopes and visible light from distant stars reach us in times consistent with a single propagation speed. If different kinds of electromagnetic waves had different velocities, pulses containing multiple frequencies would spread out dramatically over astronomical distances, which is not observed in vacuum. This supports the idea that the speed is the same for all electromagnetic waves in empty space, while their wavelengths and frequencies may differ.

Why Other Options Are Wrong:
They all have the same wavelength is incorrect because the defining difference between radio waves, visible light and X rays is their wavelength. They all have the same frequency is also wrong since frequency varies across the electromagnetic spectrum over many orders of magnitude. All of the above cannot be true because wavelength and frequency are clearly not identical for all electromagnetic waves, even though the speed is.

Common Pitfalls:
Students sometimes confuse the idea of a common speed with other properties and mistakenly think that properties like wavelength are fixed. Another confusion is between velocity in vacuum and velocity in materials such as glass, where different frequencies may travel at slightly different speeds due to dispersion. For exam purposes, always remember the simple statement: in vacuum, all electromagnetic waves travel with the same velocity c, while wavelength and frequency differ.

Final Answer:
In a vacuum, all electromagnetic waves have the same velocity.