True

Explanation:

In free space, the ratio of frequency to the velocity of light gives the phase constant. This statement is true because the phase constant is defined as the ratio of the angular frequency to the wave number, and in free space, the wave number is directly proportional to the frequency and inversely proportional to the velocity of light.

Phase Constant:

The phase constant, denoted by the symbol Φ or φ, is a parameter that represents the initial phase of a sinusoidal waveform at a specific point in space and time. It describes the position of the waveform relative to a reference point.

Angular Frequency:

The angular frequency, denoted by the symbol ω, is a measure of how quickly a sinusoidal waveform oscillates. It is defined as the rate of change of the phase of the waveform with respect to time. Mathematically, it is given by the formula ω = 2πf, where f is the frequency of the waveform.

Wave Number:

The wave number, denoted by the symbol k, is a parameter that describes the spatial variation of a sinusoidal waveform. It represents the number of wavelengths per unit distance. In free space, the wave number is given by the formula k = ω/c, where c is the velocity of light.

Ratio of Frequency to Velocity of Light:

The ratio of frequency to the velocity of light is given by the formula f/c. This ratio represents the number of cycles of the waveform that occur per unit distance traveled by light.

Relation with Phase Constant:

In free space, the phase constant is defined as the ratio of the angular frequency to the wave number, i.e., Φ = ω/k. Substituting the values of ω and k, we have Φ = (2πf)/(ω/c) = 2πfc/ω.

Since ω = 2πf, we can rewrite the equation as Φ = 2πfc/(2πf) = c. Therefore, the phase constant is equal to the velocity of light.

Hence, the statement is true.