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 .

Power is equal to work/time. The work that child 1 is performing is also equal to the change in kinetic energy. When she goes from 2m/s to 4m/s, she is increasing her kinetic energy by mv².

This is the higest number of all the given scencarios.  To arrive at this conclusion, you must compare calculations for the other given scenarios.

Power is given by . Although the student exerts a force on the books during this time, they are not moved at all, so the displacement d is 0, and thus the power is also 0.

First we can find the intensity of light in Watts per square meter, when the light reaches the window, by using .

Assuming the light spreads out evenly in all directions, it has spread out over the area of a sphere of radius 3m by the time it reaches the window.

Multiplying this intensity times the area of the window gives the power (or energy per second) leaving the window.

In physics, power is often given the unit, W, or watts. In mechanics, a watt often represents the amount of work done over a unit of time, or Joules per second.

In electrostatics a watt is expressed as the amount of current times the voltage, or as the current squared times the resistance.

A Newton-meter is a measure of energy or work, and can be written as a Joule, and is therefore the correct answer because it is not a measure of power.

The power of an elevator can be determined using the equation , with  being the work done by the elevator, and  being the time in which energy is transferred. Using this, we can plug in the known values and solve for  the power.