0

Tension T, newtons , of a string is inversely proportional to the square of the frequency, f Hz , of the note produced . When the tension is 80N , the string produces a note with frequency of 400 Hz .

When two identical strings are exerted , the ratio of the tensions is 16:81 . Find the ratio of the corresponding frequencies of the notes produced .

Here's my working:

$T= k / f^2$ where $K$ is a constant ,

$K = 80 \times 400^2 = 12800000$

$T = 12800000 / f^2 $

I think 'identical, as similar' But I do not know how to put it in a ratio form thereafter.

Shailesh
  • 3,789
user307640
  • 2,632
  • 2
  • 17
  • 27

1 Answers1

0

You really do not need to find $K$. The data about the tension $80 N$ and frequency $400 Hz$ is not needed at all.

Just write $\frac{T_1}{T_2} = \frac{f_2^2}{f_1^2}$.

So, $\frac{f_1}{f_2} = \sqrt {\frac{T_2}{T_1}} = \sqrt {\frac{81}{16}} = \color{blue}{\frac94}$

You are only asking for the ratio of the corresponding frequencies produced.

Shailesh
  • 3,789