Piano Tuning Problem: Note A on the piano has a frequency of 220 cycles/sec. Inside the piano there are two strings for this note. When the note is played, the hammer attached to the A key hits both strings and starts them vibrating. Suppose that one of the two A strings is tuned to 221 cycles/sec and the other is tuned to 219 cycles/sec. a. The combined sound of these two notes is the sum of the two sound waves. Write an equation for the combined sound wave, where the independent variable is t, in seconds. Use the (undisplaced) cosine function for each sound wave, and assume that each has an amplitude of 1. b. Use the sum in part a and transform it to a product of two sinusoids. c. Explain why the combined sound is equivalent to a sound with a frequency of 220 cycles/sec and an amplitude that varies. What is the frequency of the variable amplitude? Describe how the note sounds.
Supplements: Performance Enhancing Supplements Ergogenic aid: Any substance, mechanical aid, or training method that improves sport performance; can include supplements Supplements: pharmacologic aids used to enhance performance Supplements might give an edge but that’s it (like 1-2% increase) Not a big deal for normal people, for athletes could be a big deal NOT FDA regulated Fun facts that no one cares about or needs to know for a test Up to 11% of high school boys and 3.5% of girls have used anabolic steroids • One study found 9% of middle schoolers • Only 55% viewed use as a health risk. • 33% did not participate in formal sports • Steroid precursors – 4% of high school and 5% of college athletes • HGH – 5% of high schoolers and college athletes • Nutritional supplements – up to 88% of college athletes • Creatine 44% of high school seniors ~75% of college athletes • Ephedrine – 26% of high girls, 12% of high school boys Education vs. recommendations Quality GMP, NSF, USP stamp of approval Lab reports Proprietary vs. non-proprietary blends Reliable supplier (example: CreaPure) No guarantee but the product has been investigated and is safer You can always look at lab reports: can call company for these Proprietary Blend Clump items as a whole (18 g) Non Proprietary Blend List each item X=2 g Y=8 g, etc… Hydration Functions: • Lubrication synovial fluid eye balls, etc • Body temp regulation • Nutrient transport • Waste elimination 2 compartment:
