1. Using the theoretical equation for wave speed, determine by what factor the w

Question

1. Using the theoretical equation for wave speed, determine by what factor the wave speed would change if the linear mass density of the string were doubled.

2. Do a rough estimate of the total force on the neck of the guitar. Show your estimated values for length of strings, frequency, wavelength, and string linear density. (no actual measuring allowed!).

3. Using the principles of part 1, discuss guitar design in context of string diameter and placement. Why not use strings of the same diameter and just vary the tension to produce different pitches? (principles include relationship between tension and speed as well as mass, wavelength, and antinodes).

Explanation / Answer

1) v = sqrt(F/linear mass density)

now if linear mass density is doubled then

v' = sqrt(F/2*linear mass density) = v/sqrt(2) = 0.7*v

so new velocity becomes 0.7 times of the original velocity

2) F = v^2*linear mass density

v = f*lambda

so F = f^2*lambda^2*linear mass density

there are 6 strings and each may have different linear mass density frequency and wavelength so total force would be the sum of all the components.

3)each string is used to produce different frequency and pitch and as such the linear mass density of each strings vary some strings are thicker than the other and some are thinner. A suitable space is left between two strings so that the waves produced do not interfere with each other and hence dont disturb the tune, so the diameter of the strings is also different which sugggests that the mass for different strings are different and the length are different too.

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