# physics

When a player's finger presses a guitar string down onto a fret, the length of the vibrating portion of the string is shortened, thereby increasing the string's fundamental frequency. The string's tension and mass per unit length remain unchanged.

If the unfingered length of the string is l= 65 cm, determine the positions x of the first six frets, if each fret raises the pitch of the fundamental by one musical note in comparison to the neighboring fret. On the equally tempered chromatic scale, the ratio of frequencies of neighboring notes is 2^[1/12]

1. 👍
2. 👎
3. 👁
1. 2^1/12=1.05946

so each fret increases the frequency by that factor. But wavelength is the reciprocal of this. or w1=w*.94387

Well, to get this, one has to have adjacent frets .94387 length of the before length.

original length 65cm
next length 65*.94387
next lenght=65*(.94387)^2 and so on.

1. 👍
2. 👎
👤
bobpursley
2. thats a very good observation., i tried to look up the formula and couldn't find it.. the formula "2^[1/12]" that you posted.. there was no mention. so i started using the computer to determine trhe correct number and i came up with .94387 after writing a script using trial and error,, that yielded that number which i searched for and found this blog. thanks .. yet disturbingly while i was searching ,, i got a lot of search results about Pythagoras using the fundamental frequency and the some vague inference that he used the 3rd and 5th harmonics to make chords. but they seemed to divert from the fact that, that made it obvious that he would have built a mini harp and tuned the strings so that he could play the fundamental key for the 3rd and 5th harmonics of the third and 5th harmonics of every chord. which could have only in the end have perfectly yielded every single note in a 12 note even temperament .. but they want to credit this to some German in the 1800's. someone is trying to plagiarize the work of Pythagoras but that formula is really the one i needed , thanks

1. 👍
2. 👎

## Similar Questions

1. ### Physics

A guitar string is 90cm long and has a mass of 3.8g . The distance from the bridge to the support post is L=62cm , and the string is under a tension of 540N . What are the frequencies of the fundamental and first two overtones?

2. ### Physics

Please someone help me I'm desperate!!!! Two steel guitar strings have the same length. String A has a diameter of 0.59 mm and is under 420.0 N of tension. String B has a diameter of 1.3 mm and is under a tension of 840.0N . Find

3. ### Physics

Suppose you pluck a string on a guitar and it produces the note A at a frequency of 440 Hz. Now, you press your finger down on the string against one of the frets, making this point the new end of the string. The newly shortened

4. ### Physic

A violin string has a standard length of 32.8 cm. It sounds the musical note A (440Hz) when played without fingering. How far from the end of the string should you place your finger to play the note C (523Hz)? answer should be in

1. ### physics(HELP)

An unfingered guitar string is 0.73m long and is tuned to play E above middle C (330 Hz.) (a) How far from the end of this string must a fret (and your finger) be placed to play A above middle C (440 Hz)? (b) What is the

2. ### physics

A particular guitar string is supposed to vibrate at 210Hz , but it is measured to vibrate at 220Hz By what percent should the tension in the string be changed to correct the frequency?

3. ### physics

A guitar string is 92 cm long and has a mass of 3.7 g. The length L from the bridge to the support post is 65 cm, and the string is under a tension of 570 N. What is the frequency of the fundamental tone thanks!

4. ### Algebra

The ratio of the lengths of strings that play the guitar notes D and B is 27 to 16. If a string 64 cm long plays a B, what is the length of the string that plays a D?

1. ### Physics

A guitar string vibrates at 400 Hz and has a length of 0.8 m. Find the new frequency if a. the string is lengthened to 0.9 m. b. the string is replaced with another string, the density of which is greater by a factor of two. c.

2. ### algebra

The ratio of the lengths of strings that play the notes D and B (on a guitar), is 27 to 16. If a string 64 cm long plays B, what is the length of the string that plays a D?

3. ### math

Mrs lim had a ball of string of length 26 m. she cut 5 m of string to tie up some parcels. the remaining string was then cut into 4 equal pieces. what is the length of each piece of string?

4. ### Physics

1. A fisherman's scale stretches 3.6 cm when a 2.5-kg fish hangs from it. What will be the frequency of oscillation if the fish is pulled down 2.7 cm more and released so that it oscillates up and down? 2. Two trains emit 518 Hz