How Do You Calculate Fret Placement and Overtones in Musical Instruments?

[jrd007]

1) An unfingered guitar string is 0.73 m long and is tuned to play E above middle C (330 Hz). (a) How from from the end of the string must a fret (and your finger) be placed to play A above middle C (440 Hz)? (b) What is the wavelength on the string of this 440-Hz wave? (c) What are the frequency and wavelength of sound in air at 20 degree's C by this fingered string? Answers: a) 0.18 m, b) 1.1 m c) 440 Hz and 0.78 m

I am really stuck. All I can figure is that you incorporate L = v/2f... and f = v/wavelength... help me, please.

2) How many overtones are present within the audible range for a 2.14-m-long organ pipe at 20 degree's if (a) it is open (b) it is closed. Answers: a) 248 overtones, 249 overtones

What I thought you could do was v/2L and v/4L... 343/(2 x 2.14) = 80 and 40... not correct.

 

[Astronuc]

See if these examples help - http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/u11l5b.html

To get a higher pitch, one has to shorten the length of the string.

Try f₁ * L₁ = f₂ * L₂, where f is frequency, and then the finger is place x = L₁ - L₂, and I think you can handle it from here.

 

[jrd007]

So I would use.

.73 m x 330 Hz = L2 x 440 Hz.

L2 = .547 not the same as the answer 1...

 

[jrd007]

Anyone else have a suggestion?

 

[jrd007]

Can someone please help me with these problems? :( It is due soon.