Q16DQ - University Physics with Modern Physics

Question

If you stretch a rubber band and pluck it, you hear a (somewhat) musical tone. How does the frequency of this tone change as you stretch the rubber band further? (Try it!) Does this agree with Eq. (15.35) for a string fixed at both ends? Explain.

Step-by-Step Solution

Answer

When the rubber band is stretched, the frequency of the tone produced will increases. 

STEP1: Concept of frequency of a tone.

The length of the rubber band and the tension that is created inside of it determine the frequency of the tone. The frequency varies as a result of the rubber band being stretched.

STEP 2: Formula of frequency of the string .

If we stretch the string then its length increases and the tension in the spring also increase. The frequency of the tone depends upon both tension and length of the rubber band which can be represented by the expression given below,  

$\mathrm{f}=\frac{1}{2\mathrm{L}}\sqrt{\frac{\mathrm{F}}{\mathrm{\mu }}}$ 

 

Here, f is the frequency of the wave, L is the length of a rubber band, F is the tension in the rubber band.  $\mu$ is the mass per unit length.

 

Therefore, when the rubber band is stretched, the frequency of the tone produced will increases.