A fighter jet is traveling at 515 m / s directly away from a communication antenna that broadcas

A fighter jet is traveling at 515 m / s directly away from a...

Key Concepts

Doppler Effect

The Doppler Effect is the phenomenon where the observed frequency of a wave changes due to relative motion between the source and the observer. This concept is crucial in understanding how the motion of either party leads to a measurable frequency shift, whether the wave is sound or electromagnetic radiation.

Relative Motion

Relative Motion refers to the idea that the effects observed, such as a change in frequency, depend on the motion of the observer with respect to the source. When the observer is moving away from the source, the frequency tends to decrease, and when moving toward it, the frequency increases. This principle is the basis of the Doppler shift.

Non-Relativistic Approximation

The Non-Relativistic Approximation is used when the speed of the moving object is much less than the speed of light. In such cases, simpler mathematical formulas can be applied to calculate the Doppler shift without the need for complex relativistic corrections, making it easier to analyze frequency changes in many practical situations.

Frequency Shift Calculation

Frequency Shift Calculation involves determining the amount by which the observed frequency of a wave differs from its original frequency due to relative motion. In the context of electromagnetic waves and under the non-relativistic assumption, the shift is computed by multiplying the original frequency by the ratio of the observer's speed to the speed of light.

Transcript

00:01 Okay, we have a fighter jet that is traveling at 515 meters per second directly away from a source that is broadcasting at 406 megahertz.

00:23 If you always forget your si prefixes, you can always look them up in a table.

00:28 What change in frequency does a fighter jet observe? okay? we know that due to the doppler shift, the frequency the fighter jet will observe, which we label f prime, is equal to the actual frequency we were transmitting at multiplied times 1 plus or minus u over c.

00:53 Where u is the relative speed between the object that's transmitting and the fighter jet and c is the speed of light okay notice that this problem isn't asking us to find f prime the frequency that the fighter jet observes it's asking us to find what change in frequency does the fighter jet observe okay so f prime is going to be equal to f plus delta f.

01:28 We need to find this delta f, this change.

01:32 Okay, fortunately for us, this is actually pretty easy.

01:35 This is going to be equal to f plus or minus f times u over c.

01:43 So this quantity right here is the delta f, the change in frequency that we're trying to solve for.

01:54 Okay, so first thing first let's figure out if this is positive or negative okay so the doppler frequency increases so frequency goes up when something is getting closer okay that's when we use the positive sign the frequency is going down when something is getting farther that's when we use the negative sign okay in our problem the fighter jet is traveling away from the antenna.

02:30 So we're going to use the negative sign.

02:34 Okay? we already know what f is.

02:36 F is what the antenna was broadcasting at.

02:39 That's 406 megahertz.

02:47 Okay.

02:47 And a mega, actually we'll skip the prefixes for now.

02:53 We know that a megahertz is 10 to the 6 hertz...