Physics 341

Physics of Music

Math Status Test

truein Name:

The following questions are to give me an idea of what the mathematical and musical sophistication is of the people in this class. The level of mathematics tested here is very roughly the level expected of you during this course. This test is primarily so that I will know the level to use in teaching the class. I neither want to bore you with elaborate explanations of concepts which are well known to you, nor snow you with math that you have long forgotten. This test does not count for anything and is for my information only. Please answer as many questions as you can (guess if you have some feeling that you know what the question means).

1. $5^2=25$

2. $\sqrt{81}=9$

3. $(36)^{1/2}=6$ The notation of a number to the power 1/2 is just the same as the square root.

4. Write out in full decimal notation

        

   (a) $3.1\times 10^{2}=310$

        

   (b) $5.7\times 10^{-3}=.0057$

5. Solve for $x$ in each of the following equations:

        a)

   
   

   $$5x-8=7$$

   
   

   
   

   $$\Rightarrow x=3$$

   
   

        b)

   
   

   $$a x +b = c$$

   
   

   
   

   $$x= {(c-b)\over a}$$

   
   

6. $\sqrt{a^2\over b^4}$
   
   $${a\over b^2}$$
   
   

7. What is the meaning of $\pi$? What is the approximate value of $\pi$.

   $\pi$ is the ratio of the circumference of a circle to the diameter of the circle. Its value is appoximately 3.14

8. In the following graph, a function y(x) is plotted against x. Answer the following questions about this graph.

   =4in

        

   (a) If $x$ has value 2 what is the yalue of $y$?

   
   

   $$y=3$$

   
   

        

   (b) If $y$ has the value 5, what are the possible values of $x$? There are two values of x for which y has the value 5, namely $x=-1$ and $x=4$

9. Sketch the graph for the function $y=x^2$. =6in =3in

10. Sketch the graph for the function y=sin$(x)$. =6in =3in

11. What is the name of the note an octave above middle C? C

    
    

12. What is the name of the note a perfect fifth above A? E

    A perfect fifth below? D

    
    

13. What is the name of the note a major sixth above G? E

    A minor sixth below G? B

    
    

14. Do/did you play a musical instument? If so which and how long have you played?

    Well, I used to play violin until I was about 17. I also played a bit of clarinet.

15. Why did you decide to take this course? What do you hope to get out of this course?

    I find it a lot of fun to teach the course and I usually learn a lot about how physics and sound/music relate to each other.