SOLUTION: The rate of vibration (in oscillations per second) V of a string under constant tension varies inversely with the length L. (a) If a string is 33 inches long

Question 1075044: The rate of vibration (in oscillations per second) V of a string under constant
tension varies inversely with the length L.
(a) If a string is 33 inches long and vibrates 690 times per second, find a function
that relates the rate of vibration to the length of a string.
(b) What is the rate of vibration of a string that is 46 inches long?
Answer by ikleyn(52810) (Show Source): You can put this solution on YOUR website!
.
The "rate of vibration" is very bad term.

It is NEVER used. Let me tell you (under the secret) that such a term DOES NOT EXIST.

The number of oscillations per second is FREQUENCY.

It is the standard naming for this conception.

Solution

The condition says that the frequency f is

f = k/L,

where k is the constant coefficient, L is the length of the string.

Additionally, the condition says that 


690 = ,   which gives  k = .


Thus  f = .

If L = 46 inches, then the frequency is

f = .


Calculate.

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SOLUTION: The rate of vibration&#8203; (in oscillations per&#8203; second) V of a string under constant tension varies inversely with the length L. &#8203;(a) If a string is 33 inches long

SOLUTION: The rate of vibration (in oscillations per second) V of a string under constant tension varies inversely with the length L. (a) If a string is 33 inches long