Question

Determine which of the following signals are periodic and if so, determine their fundamental period.

a) sin [30/105πn+4]

Answer 1

The amplitude of the electromagnetic wave is 30 V/m, the frequency is 2.0 MHz, and the period is 500 ns. A graph of the wave would show a sinusoidal pattern oscillating with the given amplitude and period.

Step-by-step explanation:

The signal sin [30/105πn+4] appears to be a mathematical function which typically would be discussed in a Mathematics context; however, within the context provided, it seems to be part of a Physics question regarding the characterization of waves, specifically an electromagnetic wave with a given electric field. Nonetheless, the periodic nature and fundamental period of the signal cannot be determined without additional information, as it seems to be incomplete as presented. On the other hand, when discussing the electromagnetic wave where the electric field is given by E = (30) sin (4.0×106t), we can determine its characteristics. The amplitude is the maximum value of the electric field, which in this case is 30 V/m. The angular frequency (ω) is given as 4.0×106 rad/s, and the frequency (f) can be found by dividing the angular frequency by 2π, yielding a value of 2.0 MHz (megahertz). The fundamental period (T) of the wave, which is the duration of one complete cycle of the wave, is the inverse of frequency, resulting in T = 1/f or 5.0×10-7 s (500 nanoseconds).

To represent the signal graphically, plot electric field strength (E) on the y-axis versus time (t) on the x-axis. The resulting graph will be a sinusoidal wave oscillating between +30 V/m and -30 V/m with a period of 500 ns.

Answer 2

The student's question involves analyzing a sinusoidal wave to determine its periodicity and fundamental period, as well as finding amplitude, frequency, and period of an electromagnetic wave. More context is needed to fully resolve the first part, but the electromagnetic wave has an amplitude of 30 V/m, a frequency of 4.0 MHz, and a period of 0.25 μs.

Step-by-step explanation:

The student is asking about the characteristics of sinusoidal waves, focusing on periodicity, fundamental periods, amplitude, frequency, and the period of the waves.

For the function sin [30/105πn+4], to determine if the signal is periodic and its fundamental period, one must look at the argument of the sine function. However, more context is needed to accurately provide this information.

Concerning the electromagnetic wave with an electric field described by E = (30) sin (4.0×106t), the amplitude is 30 V/m, the frequency is 4.0 MHz (since the angular frequency ω = 2πf, and ω is given as 4.0×106 rad/s), and the period (T) is the inverse of the frequency, which is 0.25 × 10-6 s or 0.25 μs. A graph of this electric field would show a sinusoidal wave with these properties.