Question 1075044
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The "rate of vibration" is very bad term.


It is NEVER used. &nbsp;Let me tell you &nbsp;(under the secret) &nbsp;that such a term &nbsp;<U>DOES NOT EXIST</U>.


The number of oscillations per second is &nbsp;FREQUENCY.


It is the standard naming for this conception.



<U>Solution</U>


<pre>
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 = {{{k/33}}},   which gives  k = {{{690*33}}}.


Thus  f = {{{(690*33)/L}}}.

If L = 46 inches, then the frequency is

f = {{{(690*33)/46}}}.


Calculate.
</pre>