Math

CalculusPrecalculus: Mathematics for Calculus - 6th EditionThe equation that depicts the frequency of a given vibrating string which is under constant tension f and varies inversely with respect to its length l and use it to find out the length the string must be shortened to vibrate with f = 660 if the violin string is 12 inches long when f = 440Start your trial now! First week only $4.99!*arrow_forward*

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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1, Problem 136RE

To determine

**To calculate:**The equation that depicts the frequency of a given vibrating string which is under constant tension

Expert Solution

The string must be shortened to

**Given information:**

Here, the frequency of a given vibrating string which is under constant tension

Also, violin string is

New frequency is

**Formula used:**

For 2 variables say,

Which can be written as:

Where

Similarly the statement

Which can be written as:

Where

**Calculation:**

As the frequency of a given vibrating string which is under constant tension

Recall, For 2 variables say,

Which can be written as:

Where

Hence, this variation can be expressed as follows:

Where

It is also given

Put these values in

Therefore, the proportionality constant

Now for new frequency of vibrating string

Replace the value of

Thus, the string must be shortened to