Question

If the tension in a string doubled, then a natural frequency will increase decrease by If the 3^rd harmonic has a frequency of 600Hz, the frequency of the fundamental is Two strings have the same length and tension. One string has a mass per length that is 4 times that of the other string. The fundamental frequency of the more massive string will be times larger smaller than that of the less massive string. A musician playing a string instrument may use a finger to pus ha string tightly against the fingerboard of her instrument, thus shortening the length of the string. This causes the fundamental frequency to increase decrease not change If you take 42.0 meters of string and ball it up and put it on a scale you measure that it weighs 18.8 grams. If you tighten a length of this same string to a tension of 8.5 Newtons, what is the wave speed for waves that would travel on this string when you plucked it?

Answer 1

1) the frequency will increase if the tension is doubled as f $\oe$ sqrt(T)

2) f_n = n • f₁   so. f₁ = f₃/3 = 600/3 =200Hz

3) the frequency of the more massive string will be 1/2 of the frequency of the less massive string

as f = (1/2L)sqrt (T/(m/L))

4) increase in the natural frequency as from the above relation, we can see that frequency is inversely proportional to sqrt(L)

5) v = sqrt (T/(m/L)) = sqrt[ 8.5/(0.188/42)] =43.58m/s