The frequency of vibrations of a vibrating violin string is given by 21 V P where L is the length of the string, T is its tension, and p is its linear density.t (a) Find the rate of change of the frequency with respect to the following. (1) the length (when T and p are constant) (ii) the tension (when L and p are constant)

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Please answer part B of the question

The frequency of vibrations of a vibrating violin string is given by
1
f =
2L
where L is the length of the string, T is its tension, and p is its linear density.t
(a) Find the rate of change of the frequency with respect to the following.
(i) the length (when T and p are constant)
(ii) the tension (when L and p are constant)
(iii) the linear density (when L and T are constant)
(b) The pitch of a note (how high or low the note sounds) is determined by the frequency f. (The higher the frequency, the higher the pitch.) Use the signs of the derivatives in part (a) to
determine what happens to the pitch of a note for the following.
(i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates
df
? v0 and L is ---Select--- v= f is ---Select--- v= ---Select--- v
dL
(ii) when the tension is increased by turning a tuning peg
df
? v0 and T is ---Select--- ♥
dT
» f is ---Select--- v = ---Select--- v
(iii) when the linear density is increased by switching to another string
df
?
dp
0 and
is
-Select---
» f is ---Select--- v
---Select--- v
Transcribed Image Text:The frequency of vibrations of a vibrating violin string is given by 1 f = 2L where L is the length of the string, T is its tension, and p is its linear density.t (a) Find the rate of change of the frequency with respect to the following. (i) the length (when T and p are constant) (ii) the tension (when L and p are constant) (iii) the linear density (when L and T are constant) (b) The pitch of a note (how high or low the note sounds) is determined by the frequency f. (The higher the frequency, the higher the pitch.) Use the signs of the derivatives in part (a) to determine what happens to the pitch of a note for the following. (i) when the effective length of a string is decreased by placing a finger on the string so a shorter portion of the string vibrates df ? v0 and L is ---Select--- v= f is ---Select--- v= ---Select--- v dL (ii) when the tension is increased by turning a tuning peg df ? v0 and T is ---Select--- ♥ dT » f is ---Select--- v = ---Select--- v (iii) when the linear density is increased by switching to another string df ? dp 0 and is -Select--- » f is ---Select--- v ---Select--- v
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