Question

A string 1.0 m long produces a sound of 480 Hz. How many vibrations per second will be produced if the string is:A. 33.3 cm longB. 25 cm longC. 50 cm longD. 10 cm long

Answer 1

The frequency of a string is inversely proportional to its length, so we can write the following relation:

`f\cdot L=k`

For f = 480 Hz and L = 1 m, we have:

`k=480\cdot1=480`

Now, let's find the frequency for the following lengths:

A. 33.3 cm:

`\begin{gathered} f\cdot0.333=480 \\ f=1440\text{ Hz} \end{gathered}`

B. 25 cm:

`\begin{gathered} f\cdot0.25=480 \\ f=1920\text{ Hz} \end{gathered}`

C. 50 cm:

`\begin{gathered} f\cdot0.5=480 \\ f=960\text{ Hz} \end{gathered}`

D. 10 cm:

`\begin{gathered} f\cdot0.1=480 \\ f=4800\text{ Hz} \end{gathered}`