Graphing the superposition of three waves

[Jettaisthebes]

Hello, I have no idea how to do this problem! I have solved all my homework 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. \

PLEASE HELP! THANK YOU.. MUCH APPRECIATED..

 

[grzz]

let us suppose it is a sin wave.

Try writing down the equation for the fundamental.

My next step will then follow your post.

 

[Jettaisthebes]

for fundamental do you mean this equation.. y(x,t)=Asin(kx-wt)

 

[grzz]

We can just use y(t) = Asinwt or y = Asin(2pift).

Now try adding to the above the next two overtones.

 

[Jettaisthebes]

well have the amplitude isn't is 1/2Asinwt and then 1/3Asinwt??

 

[grzz]

well have the amplitude isn't is 1/2Asinwt and then 1/3Asinwt??

But the w is only for the fundamental. The overtones have a different w.

 

[Jettaisthebes]

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?

 

[grzz]

Is 370 in Hz?

 

[Jettaisthebes]

Well according to the problem they say the frequency.. so I'm assuming there all in Hertz.

 

[grzz]

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?

But $\omega$ is not 370 because $\omega$ = 2$\pi$f.

Hence instead of $\omega$t write 2$\pi$ft.

 

[Jettaisthebes]

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)

 

[grzz]

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.

 

[Jettaisthebes]

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??

 

[grzz]

$^{}$

The x-axis is really a time-axis and the values for the time are given. Do not forget the 10$^{-3}$

 

[Jettaisthebes]

Okay so I just substitute 10^-3 s to each t in the equation above.. ?? Sorry graphing is not quite my expertise..

 

[grzz]

t-values:

0.2 x 10$^{-3}$s

0.4 x 10$^{-3}$s

.. .. .. ..

2.6 x 10$^{-3}$s