Explaining Density
2 answers:
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The fundamental frequency on a vibrating string is given by:
where
L is the length of the string
T is the tension
is the mass per unit length of the string
Keeping this equation in mind, we can now answer the various parts of the question:
(a) The fundamental frequency will halve
In this case, the length of the string is doubled:
L' = 2L
Substituting into the expression of the fundamental frequency, we find the new frequency:
So, the fundamental frequency will halve.
(b) the fundamental frequency will decrease by a factor
In this case, the mass per unit length is doubled:
Substituting into the expression of the fundamental frequency, we find the new frequency:
So, the fundamental frequency will decrease by a factor .
(c) the fundamental frequency will increase by a factor
In this case, the tension is doubled:
Substituting into the expression of the fundamental frequency, we find the new frequency:
So, the fundamental frequency will increase by a factor .