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The Physics of Waves

Learn how frequency, wavelength, and wave speed are interconnected through a mathematical formula. Discover how to apply the formula triangle to solve wave speed problems easily and accurately in this comprehensive guide. Engage in interactive demonstrations and exercises to deepen your understanding of wave math concepts.

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The Physics of Waves

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  1. The Physics of Waves Wave Math 9-12 Science Std: Phys 4b

  2. Did you notice…… • Did you know that the things we measured work together? The frequency, the wavelength and the speed of the waves depend on each other There is a math formula that shows how they work together velocity = frequency x wavelength or (math equation time) v = f x λ

  3. So how does this work? • Remember the demonstration where we made standing waves You started out slow – making a standing wave that had 2 crests and 3 nodes count the number of times your hand moved to find the frequency measure the wavelength

  4. So how does this work? • Remember the demonstration where we made standing waves Then you went faster, making a standing wave that had 3 crests and 4 nodes Did you notice that the wavelength got shorter? And the number of times your hand moved went up so the frequency went up?

  5. So how does this work? • Remember the demonstration where we made standing waves Finally, you went the fastest and made a standing wave with 4 crests and 5 nodes And the wavelength got even shorter? And the frequency went even higher?

  6. So how does this work? • In fact, if the frequency doubled (2x)….. The wavelength was cut in ½ We can see this in the formula: v = f x λ If the velocity stays constant Every time the frequency goes up The wavelength goes down

  7. Here’s an easy way to work it… • Remember the “Formula Triangle” The other side of the formula goes on the bottom of the triangle with one part in each box In the formula triangle, one side of the formula goes up in the top

  8. Here’s an easy way to work it… • Remember the “Formula Triangle” And they equal the top section The lower section items are multiplied together = X

  9. Here’s an easy way to work it… • So for the formula v = f x λ And they equal the top item The two items on the bottom are multiplied together V = f λ X

  10. Here’s an easy way to work it… • If you are missing one of the lower parts And they equal the missing bottom item You can divide the top part by the lower part you have V ∕ f λ =

  11. An example with numbers…. • If the frequency is 5hz and the wavelength is 0.75m What is the speed of the wave? And using the triangle, solve for what we don’t know Use the equation v = fλand fill in the triangle V 3.75 m/s V = 5hz x 0.75m Fill in the numbers we know….. V = 3.75 m/s X hz = 1/sec f λ 5 hz 0.75m

  12. How about another…. • If the wavelength is 1.0m and the speed is 7 m/s What is the frequency of the wave? And using the triangle, solve for what we don’t know Use the equation v = fλand fill in the triangle V 7.0 m/s f = 7.0m/s / 1.0m / f = 7.0 1/s Fill in the numbers we know….. hz = 1/sec f λ 7 hz 1.0m

  13. So why don’t you try some….. • Remember to use the formula triangle to help you A string is vibrating at a frequency of 200 hz and has a wavelength of 0.5 m. What is the speed of the wave? A slinky has a wave speed of 10 m/s. You see a wavelength of 150 cm. What is the frequency of the wave? V f λ Work together at your tables and we will check your answers in a little bit

  14. So why don’t you try some….. • Remember to use the formula triangle to help you A string is vibrating at a frequency of 200 hz and has a wavelength of 0.5 m. What is the speed of the wave? A slinky has a wave speed of 10 m/s. You see a wavelength of 150 cm. What is the frequency of the wave? V V = fλ X V = (200hz)(0.5m) f λ V = 100 m/s Work together at your tables and we will check your answers in a little bit

  15. So why don’t you try some….. • Remember to use the formula triangle to help you A string is vibrating at a frequency of 200 hz and has a wavelength of 0.5 m. What is the speed of the wave? A slinky has a wave speed of 10 m/s. You see a wavelength of 150 cm. What is the frequency of the wave? V / V = fλ X V = (200hz)(0.5m) f λ V = 100 m/s f = v/λ f = (10m/s)/(1.5m) f = 6.66 hz

  16. Questions?

  17. When we made waves • We made 2 types of waves: • Transverse waves • These are waves that move back and forth perpendicular to the way the wave is traveling

  18. When we made waves • We made 2 types of waves: • Longitudinal waves • Also called compression waves, these move in the same direction as the wave is traveling

  19. We looked at the parts of a wave • Crest • Trough • Amplitude • Wavelength

  20. And we counted the frequency Remember that the frequency is the count of how many times a wavelength goes by in one time interval (normally, the # of crests per second)

  21. We even talked about the period The period is a measure of the amount of time it takes for one wavelength to go by

  22. We made single pulses and standing waves • We even measured the standing waves and started doing some math with what we measured

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