A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to Figure 6.4, answer the following: (a) Estimate the wavelength of this radiation.

Video transcript

hey everyone in this example it says that a majority of five G networks rely on the spectrum in the 3.5 gigahertz range. We need to calculate the average wavelength that is used. So based on our prompt were given a value in units of gigahertz and we can interpret this as a frequency which we recall is represented by the following symbol and is in units of hertz or inverse seconds. The prompt also mentioned us calculating average wavelength, recall that wavelength is represented by the symbol lambda. And so the only other variable that connects these values is our speed of light. So we should recall that our formula for the speed of light is equal to our wave length, multiplied by our frequency. So define our wavelength or average wavelength. We're going to find that by taking lambda and setting that equal to the speed of light in the numerator divided by our frequency. So our next step is to go ahead and convert our given frequency 3.5 GHz to the proper units. And hurts. So we're just going to go ahead and actually do the conversion here. We're going to multiply By our conversion factor to get two Hz going from gigahertz. And we should recall that are prefixed giga tells us that we have for one gigahertz to the ninth power hurts. So this gives us our frequency equal to a value of 3. times 10 to the ninth power hertz, which we can also interpret as inverse seconds because they're equivalent units. So moving into our calculation for our wavelength, we would recall that in our numerator, our speed of light is going to be three point oh times 10 to the eighth power meters per second as our units. And then in our denominator we're going to plug in that frequency as 3.5 times to the ninth power inverse seconds, so that we can cancel out our units of seconds. So this leaves us with units of meters. And when we take the value of this quotient, we're going to get our value for wavelength equal to 8. times 10 to the negative second power units of m. And this would be our final answer as our average wavelength to complete this example. So I hope that everything I explained was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.