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Graphing the superposition of three waves

  1. Oct 19, 2011 #1
    Hello, I have no idea how to do this problem! I have solved all my hw problems except this one can someone please help!

    Suppose a singer singing F# (370 , the fundamental frequency) has one overtone of frequency 740 with half the amplitude of the fundamental and another overtone of frequency 1110 having one-third the amplitude of the fundamental.Graph the superposition of these three waves to show the complex sound wave produced by this singer.

    They give us a graph like with the y-axis titled displacement and the points range from 1.4 to -1.4. From 0.0 to 0.2 to 0.4 to 0.6.....1.4. On the x-axis they have it labeled as t,X 10^-3s and only display the right side so they positive part of the x-axis with points 0.2 to 2.6. \

  2. jcsd
  3. Oct 19, 2011 #2
    let us suppose it is a sin wave.

    Try writing down the equation for the fundamental.

    My next step will then follow your post.
  4. Oct 19, 2011 #3
    for fundamental do you mean this equation.. y(x,t)=Asin(kx-wt)
  5. Oct 19, 2011 #4
    We can just use y(t) = Asinwt or y = Asin(2pift).

    Now try adding to the above the next two overtones.
  6. Oct 19, 2011 #5
    well have the amplitude isn't is 1/2Asinwt and then 1/3Asinwt??
  7. Oct 19, 2011 #6
    But the w is only for the fundamental. The overtones have a different w.
  8. Oct 19, 2011 #7
    so, for the first overtone we have Asinwt for the second 1/2Asin(740)t and for the third we have 1/3Asin(1110)t.. also since 370 is the fundamental frequency can we write Asin(370)t?
  9. Oct 19, 2011 #8
    Is 370 in Hz?
  10. Oct 19, 2011 #9
    Well according to the problem they say the frequency.. so I'm assuming there all in Hertz.
  11. Oct 19, 2011 #10
    But [itex]\omega[/itex] is not 370 because [itex]\omega[/itex] = 2[itex]\pi[/itex]f.

    Hence instead of [itex]\omega[/itex]t write 2[itex]\pi[/itex]ft.
  12. Oct 19, 2011 #11
    hmmmm.. I know we can use either or but.. this should be this way: y=Asin(2pift) where y=Asin(2pi(370)t) .... etc.. y=Asin(2pi(740)t).. etc y= Asin(2pi(1110)t)
  13. Oct 19, 2011 #12
    Just add all three terms but do not forget to make the first overtone with (1/2)A and the next overtone with (1/3)A. Then substitute the values for the time required for the graph.
  14. Oct 19, 2011 #13
    okay so I will have Y=Asin2pi(370)t + 1/2Asin2pi(740)t + 1/3Asin2pi(1110)t will give me the graph.. but the values for time aren't given so can I assume 1s,2s, and 3s??
  15. Oct 19, 2011 #14
  16. Oct 19, 2011 #15
    Okay so I just substitute 10^-3 s to each t in the equation above.. ?? Sorry graphing is not quite my expertise..
  17. Oct 19, 2011 #16
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