Today's lesson involves investigating standing waves on strings. Students will read about standing waves and the relationships between wavelength, wave speed, and frequency. They will explore how changing the string length or tension affects these variables. The class will then solve sample problems applying the equations f=v/λ and L=nλ/2, where f is frequency, v is wave speed, λ is wavelength, L is string length, and n is the number of antinodes.

1. Good Afternoon! Today we will: Complete Investigation 5.3 Take notes Complete a Success Criteria Check Please do before the bell: get your lab notebook get out something to write with open your textbook to pg 508

2. Investigation 5.3 Read pg 508 – 510. Pay special attention to the two different lab set-ups we will be using. 5 min

3. Investigation 5.3 Groups of 4 Materials: clamp cup pulley fishing line mass goggles SAFETY: Do not stand with your foot under the hanging mass Goggles must be worn when string is under tension

4. Wavelength, Wave Speed, and Frequency Read pg 510 – 512 As you read, be on the look-out for: the effect of wavelength on frequency & pitch the effect of wave speed on frequency & pitch 8 min

5. Wavelength, Wave Speed, and Frequency Standing Wave: also known as a stationary wave: a wave that remains in a constant position. The length of the vibrating string in the lab determined the length of your standing wave.

6. Wavelength, Wave Speed, and Frequency If your string was 40 cm, then the wavelength of the lowest frequency standing wave was 80 cm. The length of the string is always ½ the wavelength of the lowest frequency standing wave

7. Lowest Frequency Standing Wave

8. Wavelength v Frequency What were the two ways you could get a higher frequency in today’s lab? shorten the string add tension v = fλ rearrange this formula in your notes to isolate for frequency

9. Wavelength v Frequency f = v/λ Look at your lab data for steps 4 & 5. Does your data reflect this relationship between wavelength and frequency?

10. Wavelength v Frequency f = v/λ The relationship between wavelength and frequency is inverse. In an inverse relationship, decreasing one variable (such as wavelength)increases the other (in this case, frequency)

11. Tension v Frequency Think back to the first lab we did with the string, pulley, clamp, and mass. What effect did tension have on pitch? increasing the tension increased the pitch

12. Tension v Frequency Increasing tension did not change the wavelength! So how does increased tension result in an increased pitch? increased tension on the string increases the wave speed

13. Wave Speed v Frequency f = v/λ Looking at the formula, what happens if λ is held constant while velocity is increased? frequency is increased

14. Wave Speed v Frequency f = v/λ The relationship between wave speed and frequency is a direct relationship. In a direct relationship, when one variable is increased, the other variable increases as well.

15. Good Afternoon! Today, we will: finish up our notes solve some wave problems do PTG 5_3 Please accomplish BEFORE the bell: get out your notes get out something to write with

16. More Vocabulary Words Node: the point along a standing wave that has minimal amplitude Antinode: the point along a standing wave that has maximum amplitude

17. A Picture Draw this picture into your notes and label the antinodes. Notice that the string length is the same for each different wave shape!

18. Still More Vocabulary frequency number of waves per second (Hz) period amount of time it takes one wave to pass (s) frequency = # waves/time period = time/# waves

19. What are the Equations? frequency = # waves /time period = time/# waves L = nλ/2 Where L = length of vibrating string n = number of antinodes λ = wavelength

20. Sample Problems Turn in your textbook to page 513

21. Sample Problems You and your partner sit on the floor and stretch out a coiled spring to a length of 3.5 m. You shake the coiled spring so that the pattern has one antinode between the two of you. Your partner measures the time for ten vibrations and finds it to be 24.0s. What is the wavelength?

22. Sample Prob 1, part B & C & D What is the period of vibration of the wave? What is the frequency of this standing wave? What is the speed of the wave?

23. Sample Problem 2 You stretch out a coiled spring to a length of 4.0 m, and your partner generates a pulse that takes 1.2 s to go from one end of the coiled spring to the other. What is the speed of the coiled spring?

24. On Your Own You and your partner stretch out a coiled spring that is 5 meters long. Shaking the spring between the two of you produces three antinodes. Your partner measures the time for 20 vibrations and finds it to be 12 seconds. Find the wavelength, period, frequency, and speed.