1. Waves Standing Waves Review Created by Joshua Toebbe NOHS 2015

2. Doppler Effect Created by Joshua Toebbe NOHS 2015

3. Doppler Effect Lest revisit the examples from yesterday in a little more detail, and hopefully clear up some of the confusion. (For some of you this may be redundant, but be respectful for those who need it!) Created by Joshua Toebbe NOHS 2015

4. Doppler Effect Example #1: particular string has a mass of 6 kilograms and is 24 meters long. If the fundamental harmonic frequency is measured to be 4.7 cyc/sec, what is the tension on the string. Created by Joshua Toebbe NOHS 2015

5. Doppler Effect Example #1: (solution) The first thing we need to do is to identify what we are know, and what we need to know: m=6 kg l=24 m F1=4.7 cyc/sec T=? Created by Joshua Toebbe NOHS 2015

6. Doppler Effect Created by Joshua Toebbe NOHS 2015

7. Doppler Effect Created by Joshua Toebbe NOHS 2015

8. Doppler Effect Created by Joshua Toebbe NOHS 2015

9. Doppler Effect Created by Joshua Toebbe NOHS 2015

10. Doppler Effect Created by Joshua Toebbe NOHS 2015

11. Doppler Effect Created by Joshua Toebbe NOHS 2015

12. Doppler Effect Created by Joshua Toebbe NOHS 2015

13. Doppler Effect Example #2: What is the fundamental frequency for the diagram shown below? Created by Joshua Toebbe NOHS 2015 mass=3 kg

14. Doppler Effect Created by Joshua Toebbe NOHS 2015

15. Doppler Effect Created by Joshua Toebbe NOHS 2015

16. Doppler Effect Example #2: But according to the diagram, the tension is being applied by the weight of the mass which is simply F=mg Created by Joshua Toebbe NOHS 2015 mass=3 kg

17. Doppler Effect Created by Joshua Toebbe NOHS 2015

18. Doppler Effect Created by Joshua Toebbe NOHS 2015 mass=3 kg

19. Doppler Effect Created by Joshua Toebbe NOHS 2015 So lets look at what may be causing some confusion: The first confusing point is most likely my fault. I have a horrible time making sure the information in the questions is correct. Problems 8 and 9 ask you to refer to problem 1, which doesn’t make since, instead you should refer to problem 7.

20. Doppler Effect Created by Joshua Toebbe NOHS 2015 So lets look at what may be causing some confusion: Likewise in problems 10 and 11 you are asked to refer to problem 3. Instead you should refer to problem 9. Now that we have the obvious out of the way, lets take a quick look at some basic problem solving principles.

21. Doppler Effect Created by Joshua Toebbe NOHS 2015 Understanding the question: Another point that usually causes confusion is picking information out of the problem. Unfortunately there is no easy way to get better at this other than practice. When you read the problem you have to pay attention to what you are reading, rather than just calling out the words.

22. Doppler Effect Created by Joshua Toebbe NOHS 2015 Understanding the question : Re-construct the problem in your mind, or even make a sketch and label it if you need to. Words to look for are fundamental or mode; these refer to which frequency is being displayed on the string. (Remember the chart from yesterday?) This is given as a simple number in most cases or listed as the 1 st, 2 nd, 3 rd, … harmonic.

23. Doppler Effect Created by Joshua Toebbe NOHS 2015 Understanding the question : Tension is a force, so look for words like weight, stretching, applied force, etc. Linear density is the most complicated of the single variables and it is simply mass divided by length.

24. Doppler Effect Created by Joshua Toebbe NOHS 2015 Understanding the question : Also pay attention to the units being given to you. Length is measured in meters, mass in kilograms, and by now you better be able to recognize that frequency is measured in cycles per second. Force or tension is measured in newtons, and linear density in kg/m. The units that go with each term tell you what variable it represents.

25. Doppler Effect Created by Joshua Toebbe NOHS 2015 Choosing an equation Choosing which equation to use is usually the next part that causes problems. But it is actually pretty simple. Look at what variables you have, and what you need to find, then pick the equation that contains those variables. A good one to start with is the variable you are asked to find.

26. Doppler Effect Created by Joshua Toebbe NOHS 2015 Solving the equation Lastly we come to the algebra. For some of you this is less than second nature. For others it can be quite difficult. The first step to solving the equation is to locate the variable you are trying to solve for. In the previous example problem (#1) we had to solve for Tension.

27. Doppler Effect Created by Joshua Toebbe NOHS 2015 Solving the equation The next step is to see how many of these variables exist. For these equations it will always be one variable unless you are solving for length, which occurs twice in the equations.

28. Doppler Effect Created by Joshua Toebbe NOHS 2015 Solving the equation Then you need to make sure that the variable you are solving for is not in the denominator. If it is, move it out (algebraically of course, don’t simply rewrite the equation any way you want).

29. Doppler Effect Created by Joshua Toebbe NOHS 2015 Solving the equation The work backwards according to your order of operations. Do exponents need to be removed take a root. Do parenthesis need to be removed, distribute the quantities, do objects need to be added or subtracted and multiplied or divided? This will be slightly different for each variable, but the principles are all the same.

30. Doppler Effect Created by Joshua Toebbe NOHS 2015 Solving the equation After all the algebra and rearranging of equations we have done in class, you should be able to work your way through anything by now. Just work slowly, be methodical, and check your work.