Problem 1. A stretched guitar string has a fundamental frequency of 100 Hz. By h

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Problem 1. A stretched guitar string has a fundamental frequency of 100 Hz. By how much (i.e., by what factor) would you change each of the following to raise the fundamental to 500 Hz? (a) length (b) tension (c) mass per unit length (d) diameter

Problem 2. Mythbusters is (was?) a really fun, science-like TV show, and I highly recommend watching it. In this outtake clip, they also play with Rubens’ tube: http://www.youtube.com/watch?v=ynqzeIYA7Iw However, their science explanation are sometimes a bit superficial, and in this clip they make a pretty serious physics gaffe when they point out how to measure the wavelength based on the flames (and you now know enough to spot it!). Explain their error, and explain how you should measure the wavelength based on the appearance of the flames. (Hint: the more subtle part of their error is in their statement that they are looking at areas of low and high pressure reflected in the flames—technically, it’s the areas of changing and not changing pressure. Note that while I think this show is great, keep in mind that rigorous science and entertainment are not necessarily the same thing. And it’s possible to make pretty basic mistakes, even on a gazillion-dollar budget!)

Problem 3. The speed of sound is proportional to the square root of the absolute temperature, defined by Tabs = 273 + Tc, (1) where Tc is the temperature in degrees Celsius. A trumpet is tuned to B[ (466 Hz), when it is initially cold at 20C. After playing for a while, it warms up to 30C. What is the new frequency of the trumpet (i.e., how far out of tune is it)? Assume the speed of sound at 20C to be 343 m/s, and that the trumpet (and therefore the wavelength) does not change. To get started: calculate the speed of sound at the higher temperature, given that you know what it is at the lower temperature. Then if the speed of sound changes, how do frequency and wavelength change? Is one of them held fixed by the design of the trumpet?

Answer questions with complete explanations.

Explanation / Answer

1. let u = mass per unit length

=> fundamental frequency = sqrt(T/u)/2L

=> now we need to increase frequency by a factor of 5,

a) length by a factor of 1/5 or 0.2 times of initial

b) Tension by a factor of 25

c) mass per unit length by a factor of 1/25 i.e 0.04 times of initial

d) diameter, no effects

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