IntroductionThis report is to provide an overview and interpret the nature of the doppler effect. The doppler effect defines the change in frequency of a wave when there exists a relative motion between the source of that wave and observer. This precept was stated in 1842 by Christian Doppler originally for sound, but subsequently for light as well. Since then, the principle has withstood numerous attempts to be contravened by the scientific community and are now taught in classrooms across the globe. The effect sees itself constantly within the macro world around us and has its own elegant workings, controversies and modern applications, all of which are to be discussed within this report. Define frequency and wavelength for gr 9Overview of {Instructional Topic}The doppler effect can be observed when there is a set of waves moving relative to an observer. This effect can be noticed with sound, light and water waves.
Subsequently, the doppler effect is seen in phenomena such as sonic booms, surface ocean waves, and astronomical redshift. The effect is most commonly recognized by providing a scenario in which a vehicle approaches you and moves away. As the vehicle moves closer to you, you hear a noise with a higher frequency. However, as the vehicle moves away, you observe a noise with a lower frequency. Current Curriculum CoverageThe doppler effect is most commonly taught during the senior years high school. More precisely, this topic is covered briefly in grade 11 and 12 physics within Canada. Despite this being the most common case, some students (international) may have learned it earlier while a minority have never been taught the effect.
When taught, the effect is primarily talked about in terms of sound waves and secondarily in terms of water waves and redshift. It is also to be noted that the complexity of teaching varies by school district due to variations in the curriculum. However, by not introducing the more complex real life applications, the students interest in the topic may be inhibited. This leads me to believe that the subject should be taught as a entry level high school topic. More, specifically, I would target grade 9 students to provide them with a stable foundation and proceed to bolster them from that point.
Application or Relevance TodayDespite the precept being stated over 150 years ago, it is still widely relevant to this date. The doppler effect has a baffling amount of applications. However, a few stand out that are either used in everyday activity or have altered the way we perceive the world around us. Some prime applications include the effects involvement with weather readings, radar guns and the expanding universe. Firstly, weather readings are taken by weather stations by interpreting bounce back waves off of clouds, rain or objects in the atmosphere. If the clouds are moving away from the station then the frequency of the waves will decrease upon bouncing back. However, if the clouds are moving towards the station, then the frequency of the waves will increase upon its return.
Once interpreted, this can be forged into useful data to provide wind speed and direction. Likewise, the effect allows us to get an accurate reading of a moving objects velocity relative to the position of a radar gun. A prime example of this is a policeman utilizing a radar gun to detect a driver speeding through the motorway. As the driver speeds past the policeman, each wave exiting the gun has to travel has to travel an extended distance due to the increasing displacement of the driver.
Consequently, the gap between each wave increases. The margin is taken into account by the radar gun to give an accurate reading. Moreover, we see this effect being portrayed through light as well in astronomical phenomena known as redshift. In 1923, astronomer Edwin Hubble discovered that the light from remote galaxies were shifted so heavily near the red end of the light spectrum that they have to be moving away from the milky way! Simultaneously, the galaxies closer to us experienced much less of a redshift.
A mathematical formula was later constructed for this perceived shift within the light waves. This formula shows the relationship between redshift and the rate at which a galaxy or an object moves away from the earth and became known as Hubble’s constant. This formulation was crucial to the origin of the big bang theory and is still used by physicists and astronomers to this day.Theory of {Instructional Topic}Doppler Effect: Phenomena in which the moving source conceives a higher frequency for the observer if moving towards said observer and a lower frequency if the source if moving away from said observer (through the means of its produced waves).The nature of this effect is also most commonly noted through the perception of light. Since light can be described as a wave, its color changes rather than pitch relative to an observer.
Similar to sound, the wavelength becomes greater if the source is moving away from the observer and smaller if the source is getting closer. Hence, astronomers have come up with the terms red shift and blue shift respectively. This is applicable for all wavelengths of light. Likewise, this effect can also be seen using a moving object in a body of water. The object would produce waves with much smaller gaps (shorter wavelength meaning higher frequency) in the direction in which its moving. However, the opposite would be true if you were observing the waves from the opposite end.
We can also experience increased frequency through having a moving observer. If the observer is moving towards the source with a velocity, the observer will encounter the waves quicker resulting in a higher experienced frequency. While the opposite is still true, you can experience no wave interaction if you were to travel with the same speed as the wave (or greater) in the opposite direction.Based on the consensus of the Ontario curriculum, the doppler effect is taught in grades 11/12.
Despite this, it can easily be adapted to be taught as an entry level topic in high school. Despite the difficulty being harder initially, the introduction at a younger age will help develop critical thinking skills earlier on. A sample topic briefing for the grade 9 curriculum would be as follows.
Have you ever noticed a fast car zoom past you as you were walking home? Have you heard its sound as this happened? You might have noticed that the closer the car was getting to you, the louder it was. Is this some sort of magic? Nope! It’s much simpler, its the Doppler effect. The doppler effect is caused by a change in distance by whatever created the wave and whatever sees or hears the wave (creator and watcher). As the creator gets closer to the watcher while making a noise, the noise gets louder for the watcher and the pitch gets higher. This is because the waves get bunched up together close to the watcher at first but then become spaced out as the creator moves away from the watcher. Let’s say you were walking home from school and you see an ice cream truck far away.
The ice cream truck is stopped currently as it is busy serving ice cream to your friend. At the moment, there is no doppler effect as you (the watcher) and the creator are not moving. As you see the ice cream truck finish serving your friend, you start thinking about how much you love listening to the extra catchy tune it makes while it moving so you pay extra close attention this time. As the ice cream truck starts moving, you will start hearing the doppler effect in action. As the truck gets closer and closer to you, the sound will get louder and the pitch will get higher. This is because the waves in front of the ice cream truck will bunch up and will reach you at a higher frequency (different mediums and velocity will be introduced at a later year). Mathematically, the doppler effect for sound can by shown by the equationf_o=f_s (?((v±v_o)/(v?v_s )))f_o=Frequency from watcher (observer) viewv_o=Watcher (observer) speed f_s=Frequency of sourcev_s=Speed of sourcev =Speed of sound (in air)Please note, this equation will only work when v; v_s and v; v_o and we will be measuring v in metres per second! After looking closer at this equation, we can see that the frequency heard by the watcher (observer) is simply the frequency of the source multiplied by the fraction.
As for the signs, we can choose them depending on if the source is moving towards or away from the watcher(observer). Lets demonstrate this by considering the ice cream truck example above. Example: As the ice cream truck begins moving (10m/s) from your friend Bills house down the road towards you, what frequency can you expect to hear if you didn’t move from your driveway? The ice cream truck driver hears the tune at 400Hz and take v (speed of sound) to be 343m/s.Solved: f_s=400Hz v=343m/s v_o=0m/s v_s=-10m/s (negative because the ice cream truck is moving towards you, hence we need a bigger f_o)f_o=400Hz(?((343m/s)/(343m/s-10m/s)))f_o=412HzAs we expected, the frequency experienced by the watcher (observer) than that of the source!For the higher level portion of this topic, we will focus on two beam interference. Due to the intriguing relationship positive and negative relationship between light waves and electric fields, we can notice types of interference when two or more arrive in the same place.
