A standard cell phone transmits electromagnetic waves with a frequency of 1.90 × 1 0 9 H z 1.90\times10^9Hz 1.90 × 1 0 9 Hz . Calculate the wavelength of these electromagnetic waves (in cm).

Alright, folks. Welcome back. Hopefully, you had a chance to try this one on your own. So we have here that a standard cell phone transmits an electromagnetic wave at a frequency of 1.9 times 10 to the 9th Hertz. So that's our f. What we wanna do is we wanna calculate the wavelength of these electromagnetic waves, and we wanna express it in centimeters. And remember from our video, whenever you wanna convert either wavelength to frequency or frequency to wavelength, we can always do so using the equation c equals lambda times frequency. This equation only has 2 unknowns, so as long as you have one of them, you can always find the other, because remember that c is just a constant. That's just the speed of light, 3 times 10 to the 8th meters per second. So that's all we have to do. We just have to set up our equation c equals lambda times frequency, wavelength times frequency. And, let's see, we already have the frequency and we want to calculate what the lambda is, so we basically just have to move this over to the other side and then plug in some numbers. So we have that c divided by the frequency is equal to lambda. So in other words, we have 3 times 10 to the 8th meters per second, and we have to divide this by 1.9 times 10 to the 9th in Hertz. And the units will basically work out to meters. So what you get when you plug this in is you get 0.158, and that's in meters. Now we're not quite done yet because we have to convert it to centimeters, and all you have to do is just shift the decimal place to the right twice. So this basically just becomes 15.8 centimeters. Alright. So that's it for this one, folks. Let me know if you have any questions.

A standard cell phone transmits electromagnetic waves with a frequency of 1.90 × 1 0 9 H z 1.90\times10^9Hz 1.90 × 1 0 9 Hz . Calculate the wavelength of these electromagnetic waves (in cm).

5.70 × 1 0 15 c m 5.70\times10^{15}cm 5.70 × 1 0 15 c m

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32. Electromagnetic Waves

The Electromagnetic Spectrum

Physics

32. Electromagnetic Waves

The Electromagnetic Spectrum

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Multiple Choice

A standard cell phone transmits electromagnetic waves with a frequency of $1.90\times10^9Hz$ . Calculate the wavelength of these electromagnetic waves (in cm).

15.8 cm

$5.70\times10^{15}cm$

0.158 cm

0.0633 cm

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Verified step by step guidance

Identify the given frequency of the electromagnetic wave, which is $1.90 \times 10^9$ Hz.

Recall the equation that relates the speed of light $c$, wavelength $\lambda$, and frequency $f$: $c = \lambda f$.

Use the constant speed of light $c = 3.0 \times 10^8$ m/s.

Rearrange the equation to solve for wavelength $\lambda$: $\lambda = \frac{c}{f}$.

Substitute the given values into the equation: $\lambda = \frac{3.0 \times 10^8\, \text{m/s}}{1.90 \times 10^9\, \text{Hz}}$ and convert the result from meters to centimeters by multiplying by 100.