SAMPLE CHAPTER PHYSICS FOR MATRICS {STUDY GUIDE FOUR OF FOUR} BONGINKOSI MNISI BENEDICT DIDCOTT-MARR CAPS APPROVED STUDY GUIDE

Transcription

1 SAMPE CHAPTER PHYSICS FOR MATRICS {STUDY GUIDE FOUR OF FOUR} BENEDICT DIDCOTT-MARR BONGINKOSI MNISI CAPS APPROVED STUDY GUIDE

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3 DOPPER EFFECT Have you ever wondered why the siren on a moving ambulance seems to change pitch/ frequency? i) As it approaches you, ii) iii) When it is next to you, When it leaves you? Approaches YOU NEXT TO YOU EAVES YOU In this chapter we will try to answer that question. An Austrian physicist, Christian Doppler, asked himself the same question: Why does sound on a sound emitting object seem to change pitch when the object is in motion relative to you the listener/observer? He further asked, If we can answer the why, can we then ask the how mathematically? SAMPE

4 DOPPER EFFECT WITH SOUND AND UTRASOUND Sound is a wave. When an object producing sound is in motion in the air, the waves are made to stretch or compress. Depending on where and what the observer is doing relative to the sound source, he/she will hear a different pitch to the one that the sound source is emitting. Imagine a duck in a pool. When the duck is stationery, the water in the pool might ripple, and the ripples will be evenly distributed around the duck. If you were to sit anywhere around the pool with your legs in the water, the water ripples hitting you per second would be the same. Imagine now that the duck starts moving, SAMPE Notice now how the distribution of ripples is so different, in front (more ripples) and behind (less ripples). This is what Doppler meant, depending on where you are relative to the duck; you will either get hit by more ripples or less ripples. After Doppler had formalised this beautiful phenomenon mathematically, it became known as the Doppler Effect.

5 In formal terms; the Doppler Effect is defined as: Definition The apparent change in the frequency (or pitch) detected by an observer in relative motion with a source of sound, through a medium of sound propagation. In answering the how of the Doppler phenomenon, Christian Doppler proposed the Doppler equations. This is the general equation given to you in the final exam sheet: Where: Note f = Frequency at which listener hears sound V= Velocity of sound in medium - A common mistake is that of confusing changes in sound frequency with changes in sound amplitude. The Doppler Effect has nothing to do with the loudness (sound amplitude) of the sound source in consideration. By dialling up the volume knob when Changes by Klingande plays on your radio, you are merely increasing the amplitude of the sound waves from your speakers, not their frequency. If dialling up the volume changed the frequency, the voices of the singers would sound very weird (squeaky) and music would lose meaning. THE DOPPER EQUATIONS SAMPE Note: this will be given in the exam question Note f = v + v - - v + v S f S f S = Frequency of source V S = Velocity of source V = Velocity of listener In all cases we are either trying to scale up, keep the same or scale down the frequency of the source (f S ) as heard by the observer (f ). In all three cases the frequency of the source is kept constant and we have shown that (the frequency observed is directly proportional to the frequency emitted).

6 Below are the equations governing the three cases we observed and asked ourselves a question at the beginning of this chapter. Case i) Observer is stationary, source is approaching We expect the observer to hear a higher pitch/frequency since the source is approaching; just as you would get hit by more ripples per unit time if you were sitting in front of a duck that was coming towards you. And so we have that: Notice that the scaling factor { } (or you may call it the proportionality variable) is greater than 1 { >1} which means f >f S, which makes sense, the observed frequency is higher than that of the source (source is approaching)... Doppler was on to something here. Case ii) Both observer and source are stationary or moving with the same velocity SAMPE This is the simplest of the three cases as you don t expect a change in pitch since both you (the observer) and the source are not moving relative to each other and so our scaling factor here is 1, therefore: S f 0 = f ss Note If this statement confuses you in terms of the diagrams above, especially the one where the observer and the source are moving with the same velocity, revise relative motion in mechanics.

7 Case iii) Observer is stationary, source is moving away In this case we expect the observer to hear a lower pitch/frequency as the source is moving away; just as you would get hit by less ripples if you were sitting behind the duck and the duck was moving away from you. So we have: As Expected, the scaling factor is less than 1 { is less than the frequency of the source [f <f S ]. <1} but greater than zero, and the observed frequency Imagine now that the observer is moving but the source is at rest. The Doppler Effect is still observed; the physics doesn t change: i) When the observer approaches the source, he/she will hear a higher pitch, ii) iii) When the observer is stationary with the source (or allowed to move but with the same velocity of the observer), there s no change in pitch, When the observer is moving away from the source, the pitch drops. If you understand the physics, the maths will only be a joke. On page 7 we ullustrate these three cases. S SAMPE

8 Case i) Observer approaches the source, source is stationary When the observer approaches the source, the observed frequency (by the observer) is given by: Note that the scaling factor, >1 and so as expected f >f S. Case ii) Observer and source not moving relative to each other When the observer and the source are at both at rest relative to each other, the equation used as in the previous scenario is f =f S. Case iii) Observer moving away, source stationary SAMPE When the observer is moving away from the source, the observed frequency is given by: S S Notice again, the scaling factor; physics f <f S. <1 and as we expected from our understanding of the governing

9 A third scenario is when both the source and the observer are in motion. If you understand relative motion, you will notice that there is No change in the physics. We simply adopt a fancier scaling factor [ ] for the maths. The governing equation now becomes S Now the thing to remember here... well there s very little to remember, let s work out some examples and do please complete the exercises at the end of this chapter. Example 1: The Scary Character Encounter After watching two horror movies (eft Turn 1 and eft Turn 2) and for simplicity let s assume eft Turn 1 is much scarier than eft Turn 2; Mikateko and Peter (friends) are taking a walk in the woods. Mikateko (50 metres away from Peter) notices what she believes to be a character from eft Turn 2. Filled with adrenalin, she starts running towards Peter and screaming at a rather disturbing frequency of 540Hz (as heard by Peter while stationary) She runs easterly towards Peter at 4m. s -1. Peter is stationary for the first 25 metres of her (Mikateko s) run and being less scared he takes off at only 2.8m. s -1 in the same easterly direction. To be clear; Peter hears Mikateko screaming at 540Hz for the first 25 metres of her run and then takes off at her 25 metre point. Assume that the speed of sound in the wood s air is 345m. s -1. SAMPE 1.1 As a clever physics learner you probably have noticed that the frequency heard by Peter before he takes off isn t exactly the frequency with which Mikateko is screaming Name and define the physics phenomenon associated with the change in the frequency heard by Peter. S (Answer: Doppler Effect; The apparent change in the frequency (or pitch) detected by an observer in relative motion with a source of sound through a medium of sound propagation )

10 1.1.2 Say whether the frequency heard by Peter is OWER THAN, SAME AS or GREATER THAN the true frequency with which She (Mikateko) is screaming and give a reason for your answer. (Answer: Greater than, Mikateko is running towards/approaching Peter. Frequencies of approaching sources are higher.) If Mikateko was running slower, would the frequency heard by Peter be ESS THAN, EQUA TO or GREATER THAN 540Hz? (Answer: ess than) Calculate the true frequency with which Mikateko is screaming (call it f Mikateko ) 1.2 Peter takes off From your knowledge of mechanics (relative velocities), say whether the frequency heard by Peter (after taking off) is GREATER THAN, EQUA TO, ESS THAN 540Hz and give a reason for your answer. (Answer: ess than, as Peter (the observer) takes off, in his frame of reference, Mikateko (the source) appears to be moving slower, hence he will observe a frequency lower than the one he was hearing initially.) Calculate the frequency that Peter hears after he takes off. (Answer:???) SAMPE Note The source (Mikateko) is moving towards the observer and so we have a plus (+) in the numerator of our scaling factor. On the other hand, if the source was moving away from the observer we would have a minus ( ). The observer (Peter) on the other hand is moving away from the source, hence we have a plus (+) on the denominator. If he were to move towards the source, we would have a minus (-). Note the extra care for the differences in the uses of plus (+) and minus (-) for the source (numerator) and observer (denominator).

11 Example 2: Question 6 (Dept. Basic Education, Republic of SA Grade 12. Physical Sciences 2014 Exemplar). The siren of a stationary police car emits sound waves of wavelength 0,55 m. With its siren on, the police car now approaches a stationary listener at constant velocity on a straight road. Assume that the speed of sound in air is 345 m s Will the wavelength of the sound waves observed by the listener be GREATER THAN, SMAER THAN or EQUA TO 0, 55 m? (1) (Answer: Greater than, the source is approaching the observer.) 6.2 Name the phenomenon observed in QUESTION 6.1. (1) (Answer: Doppler Effect 6.3 Calculate the frequency of the sound waves observed by the listener if the car approaches him at a speed of 120 km h -1. (7) i) We must convert the given wavelength into a frequency Sound frequency and wavelength are related by the formula. And so we have that 345 m s -1 = f 0.55m F = Hz SAMPE ii) Now we need to convert the speed from km h -1 to m.s -1. iii) Hints This question has 7 marks, which should indicate to you that the examiner wants more from you than just plugging numbers into the Doppler equations. Hints V sound Hint: Always make sure you calculate with numbers that have SI units, the examiner could have used centimetres in the wavelength units, it s your task to make sure everything is in SI units. There are 1000m in a kilometre and 3600 s in 1 hour. We multiply 120 km. h -1 by 1000 and divide it by 3600 to get it to m. s -1. If you do that, you should find Vs = m. s -1. Now you can throw it all into the Doppler equations: S 6.4 How will the answer in QUESTION 6.3 change if the police car moves away from the listener at 120 km h -1? Write down only INCREASES, DECREASES or REMAINS THE SAME. (1) (Answer: Decreases)

12 DOPPER EFFECT WITH IGHT As you may or may not know, light is a wave, a special kind of wave called an electromagnetic (EM) wave with a fixed speed of about in a vacuum. The light we know/see as colours is only a fraction of a broader spectrum of electromagnetic waves called the electromagnetic spectrum. The fraction of the EM spectrum that is visible to the human eye (colours) is called the visible spectrum. The red end of the visible spectrum is characterised by longer wavelengths (lower frequencies) while the blue end has shorter wavelengths (higher frequencies). SAMPE

13 ight as a wave is also subject to the Doppler Effect; I ll tell you how. When light emitting sources are moving away from you (the observer) their light waves get stretched (light bulb) Doppler Effect, stretching means making their wavelength longer, which means the light you see is slightly shifted to the red end of the visible spectrum, this in Doppler terms is called a red shift. Similarly when light sources are moving towards you (observer) their light waves get clumped up in front of them[this means smaller wavelengths], meaning the light your observe is slightly shifted to the blue end of the visible spectrum and yes your guessed right, this is called a blue shift (illustrated above). By pointing telescopes in all directions of the night sky, astronomers (scientists) observed that most of the light from stars was red shifted... I leave you as an aspiring scientist to tell your friends what conclusion the astronomers made from their observations. SAMPE

14 SUMMARY Doppler Effect: The apparent change in the frequency (or pitch) detected by an observer/listener in relative motion with a source of sound through a medium of sound propagation. When the source is moving (listener stationary) Source The physics (what we expect) Equation to use Moving towards listener Moving away from listener Source > )))))))) istener f <f S istener ( ( ( ( Source > f <f S When the listener is moving (source stationary) istener The physics (what we expect) Equation to use Moving towards source Moving away from source istener >((((((( Source f <f S SAMPE Source) ) ) ) istener > f <f S

15 Both listener and source moving Remember the equation used in this case is: S S In the table below are four possible sub cases that you might encounter for this case: Source Moving away Moving towards Moving away from source istener Moving towards source < Source ) ) ) istener > [Source] [istener] [Source] [istener] Source > ))) < istener SAMPE

16 EXERCISES Exercise 1: Question 6 (Dept. of Basic Education, Physical Sciences P1, November 2011) A train approaches a station at a constant speed of 20 m s -1 with its whistle blowing at a frequency of 458 Hz. An observer, standing on the platform, hears a change in pitch as the train approaches, passes and moves away. 6.1 Name the phenomenon that explains the change in pitch heard by the observer. (1) 6.2 Calculate the frequency of the sound that the observer hears while the train is approaching him. Use the speed of sound in air as 340 m s -1. (4) 6.3 How will the observed frequency change as the train passes and moves away from the observer? Write down only INCREASES, DECREASES or REMAINS THE SAME. (1) 6.4 How will the frequency observed by the train driver compare to that of the sound waves emitted by the whistle? Write down only GREATER THAN, EQUA TO or ESS THAN. Give a reason for the answer. (1) SAMPE

17 Exercise 2 Question 6 (Dept. Basic Education, SA Physical Sciences P1, February/March 2013) The siren of a stationary ambulance emits sound waves at a frequency of 850 Hz. An observer, travelling in a car at a constant speed in a straight line, begins measuring the frequency of the sound waves emitted by the siren when he is at a distance x from the ambulance. The observer continues measuring the frequency as he approaches, passes and moves away from the ambulance. The results obtained are shown in the graph below. 6.1 The observed frequency suddenly changes at t = 6 s. Give a reason for this sudden change in observed frequency. Hints 6.2 Calculate the: In the first 6 second, the observed frequency is higher than the emitted frequency. There s a stepped transition at t =6s, after which the observed frequency remains constant and lower than the emitted frequency. Ask, when do I hear a high pitch and when do I hear a low one, this should tell you what happens at t =6s SAMPE Speed of the car (5) (Take the speed of sound in air as 340 m s -1.) Distance x between the car and the ambulance when the observer BEGINS measuring the frequency (3)

18 Note: The speed of the car remains constant throughout the whole experiment (if this is an experiment). Can you think of a reason for this, in terms of the graph? This should give you a hint as to which equation of motion you should use here Extension question. If the ambulance was not stationary, let s say it was moving in the same direction with the observer in the vehicle. How fast would the ambulance have to move for its siren to not change Frequency (remain at 850Hz) to the observer? SAMPE

19 It is for this reason that Voltage meters are always connected at two points (connected in parallel) across an electric component or piece of wire in a circuit; loosely put: they measure a potential at one point (V 1 ) and another point (V 2 ) and then the difference ( V or just V) is calculated and called the Potential Difference. V R If an electric charge is placed in an electric potential difference, the potential difference is capable of moving it (it can do something to it). Hints A source of an electric potential difference in a circuit (the ones we are dealing with here) is a cell. Hints + A combination of two or more cells with some internal resistance added (see resistance below) is called a battery. - SAMPE + - Current When seeing the word current, the first thing that comes to your mind is flow, and it s no surprise that your beautiful mind associates currents with flows since the word is frequently used in connection with things like air flow, water flow (in rivers and oceans) and a whole bunch of other things that flow.

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