# To express: The given variation as equation.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.11, Problem 47E

(a)

To determine

## To express: The given variation as equation.

Expert Solution

The equation of the given variation f=k/L .

### Explanation of Solution

Inverse variation:

If the quantities a and b are related by the equation a=Cb then for C0 , a is inversely proportional to b and C is called constant of proportionality.

The frequency of vibration of a violin string is inversely proportional to its length.

Mathematically,

f=k/L (1)

Thus, the equation of given variation is f=k/L .

(b)

To determine

### To find: The change in frequency when length of the string is doubled.

Expert Solution

The frequency of the vibration becomes half.

### Explanation of Solution

Given:

The length of the string is doubled.

Calculation:

To calculate frequency for double the length of string, substitute 2L for L in equation (1).

f1=k/2L (2)

Here, f1 is the frequency of vibration when length is doubled.

Compare equation (1) and equation (2).

f1=f2

Thus, the frequency for double the length becomes half.

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