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Chapter 7: Q.472. (page 741)

On a string instrument, the length of a string varies inversely with the frequency of its vibrations. If an11-inch string on a violin has a frequency of 360cycles per second.

What frequency does a12-inch string have?

Short Answer

Expert verified

The frequency will bef=330cycles per second.

Step by step solution

01

Step 1. Given information.

The length of the stringlvaries inversely with frequencyf, whenl=11inch andf=360cycles per second.

02

Step 2. Write the formula for inverse variation.

l=kf

03

Step 3. Substituting the values and finding the value of k.

l=kfk=lfk=11脳360鈰�鈰�l=11,f=360k=3960

04

Step 4. Now, find the value of f, when k=3960 and l=12.

l=kff=klf=396012f=330

05

Step 5. Simplified answer.

Hence, the frequency will be f=330cycles per second.

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