The speed of sound in dry air at 20 °C is 343 m/s and the lowest frequency sound wave that the human ear can detect is approximately 20 Hz. (b) What would be the frequency of electromagnetic radiation with the same wavelength?

Video transcript

Hello everyone. Today we have a fun problem. The speed of sound in dry air at 25 °C is 346 m per second. And the lowest frequency sound wave that the human ear can detect is approximately 20 Hertz. Calculate the frequency of electromagnetic radiation with the same wavelength as the sound wave. So we can calculate the wavelength of the sound wave using the formula for speed. Such that speed is equal to the wavelength multiplied by the frequency rearranging this equation we get at the wavelength is equal to the speed which was 346 point meters 3 46 m per second divided by hour s frequency which was 20 Hertz. However, to make this into units of seconds, we can use the conversion factor that one Hertz is equal to one over or one divided by seconds. And this gives us a wavelength of 17.3 m. So now we can find the frequency of the electromagnetic radiation with the wavelength of 17.3 meters. Using the equation that our frequency is equal to the speed of light divided by our wavelength. So we have a speed of light, which can be found on the reference text as a 3.0 times 10 to the eighth meters per second. We divide that by the wavelength that we found at the previous step, which is 17.3 m. In doing this, we cancel out our units of meters and we actually get 1.73 times 10 to the seven divided by seconds, which is equivalent to 1.73 times 10 to the seven Hertz. However, we need this in units of megahertz. So we can multiply at 1.73 times 10 to the seven Hertz by the conversion factor that one megahertz is equivalent to one times 10 to the six Hertz units of Hertz canceled out and we arrive at 17.3 megahertz. Now seeing that that is not an answer choice, we round off to the nearest one significant figure to be 20 megahertz or answer trace D as our answer overall, I hope this helped. And until next time.