pattyv9845
29.10.2019 •
Mathematics
The frequency of vibrations of a vibrating violin string isgiven by
f= 1/2l ? t/p
where l is the length of the string, t is its tension, and pis its linear density.
find the rate of change of the frequencywith respect to
a) the length (when t and p areconstant)
b) the tension (when l and p areconstant)
c) the linear density (when l and t areconstant)
d) the pitch of a note (how high or low the note sounds) is determined by the frequency f. (the higher frequency, the higher the pitch.) use the signs of the derivatives you found above to determine what happens to the pitch of a note in each of the following situations.
(i) when the effective length of a string is decreased by placing a finger on the string so a shorter portions of the string vibrates.
(ii) when the tension is increased by turning a peg.
(iii) when the linear density is increased by switching to another string.
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Ответ:
a. [tex] $f\propto L$ [\tex]
b. [tex] f \propto \sqrt{T} [\tex]
c. [tex] f \propto \frac{1}{\sqrt{P}} [\tex]
I. Decrease in length increases leads to increase in pitch.
II. Increase in tension leads to increase in pitch.
III. Increase in linear density reduces the pitch
Step-by-step explanation: I. Since the frequency is inversely proportional to the length increase in length leads to decrease in frequency likewise decrease in length leads to increase in frequency.
II. Since the frequency is directly proportional to the square root of the tension increase in tension leads to increase in frequency likewise decrease in tension leads to decrease in frequency.
III.since the frequency is inversely proportional to the square root of the linear density so increase in linear density leads to decrease in frequency and likewise decrease in linear density leads to increase in frequency.
Ответ: