The Doppler shift equation for light is , where f is the source frequency, f' is the observed frequency, v is the relative velocity between source and observer, and c is the speed of light.

When the source and observer are moving closer together, v is positive, so the observed frequency is greater than the source frequency. Greater frequency also implies shorter wavelength, so visible light is shifted towards the blue end of the spectrum.

In this scenario the Doppler effect is described by the following equation. 

Using the values from the problem, we know that v_o is zero and v_f is 15m/s. v is 340m/s and f_s is 790Hz.

The equation for Doppler effect is   , where the + sign applies when the source and observer are moving farther apart, and the - sign applies when they are moving closer together. In these equations, v is the speed of sound, 340m/s,  is the frequency of sound emitted by the source,  is the freqency perceived by the observer, and  is the relative velocity between the source and observer.

We can apply this equation to the first part of the motion, as the truck moves closer to the observer, to solve for the velocity of the truck.

Now we can plug this velocity into the equation again for when the truck moves farther away from the observer and solve for .

This question is asking us how the frequency changes when one object moves directly towards another; thus, this is a Doppler effect problem. Remembering back to our Doppler effect formula, we know that, where f is the frequency heard by the recipient (the person at the concert), v_r is the velocity of the receiver, v_s is the velocity of the source, and f₀ is the original frequency.

In our case, the speaker is not moving, so v_s is zero. v_r is positive when the person is walking towards the speaker, so the frequency heard will be higher than the original frequency.

This question is asking us how the frequency changes when one object moves directly away from another; thus, this is a Doppler effect problem. Remembering back to our Doppler effect formula, we know that, where f is the frequency heard by the recipient (the person at the concert), v_r is the velocity of the receiver, v_s is the velocity of the source, and f₀ is the original frequency. 

In our case, the speaker is not moving, so v_s is zero. v_r is negative when the person is walking towards the speaker, so the frequency heard will be lower than the original frequency. We can calculate the heard frequency using our equation.

The formula for the Doppler effect is:

Only frequency of the sound is affected by the Doppler effect; velocity and amplitude remain unchanged. When the source is moving away from the observer the velocity of the source is added to the speed of light.

This increases the value of the denominator, decreasing the value of the observed frequency. Frequency corresponds to pitch or tone; a lower observed frequency will result in a lower observed pitch.

The doppler effect states that if two objects are moving closer together, perceived frequencies for emitted waves will be higher. If you are jogging away from the car at , but the car is traveling at , the overall distance between you and the siren is decreasing. You will hear a higher frequency than what the siren is emitting.

The numerator is subtracted when the observer moves away from the source. The denominator is subtracted when the source moves toward the observer. In this problem both terms would be subtracted, but the denominator would be decreased by more than the numerator. This would result in a fraction greater than one, and an overall increase in the final frequency.

The Doppler effect accounts for observed frequency versus actual frequency emitted by a sound or light source. The equation for the Doppler effect is:

The numerator terms are summed when the observer moves toward the source, and the denominator terms are summed when the source moves away from the observer. In this question, we know that the source moves away from the observer; therefore, the observed frequency will be less than the actual frequency because the denominator in the equation will increase.

The question, however, asks about wavelength. If the frequency decreases, then the wavelength must increase according to the equation:

Velocity will remain constant (the speed of light). Any change in frequency will cause a change in wavelength via their direct relationship in the given equation.

The Doppler equation is:

.

Because the cars are approaching each other, the frquency heard will be increased. This fundamental knowledge allows you to determine the signs of the equation. The top of the fraction will be addition and the bottom will be subtraction to make a coefficient greater than 1.

Use the given values to solve:

Now that we know the frequency, we can solve for the wavelength:

In order to solve this problem we must know how to utilize the Doppler formula.

is the velocity of the observer and is the velocity of the source. Notice that the frequency must increase as the observer and source move closer, and therefore the plus sign is used in the numerator and the minus sign is used in the denominator. Had the jogger been moving away from the fire truck, the subtraction function would be used in both the top and bottom.

In this case we see that the source is the fire truck, moving at , and the observer is the jogger, moving at . By plugging these numbers into the formula and  for , we find the perceived frequency or to be .