Screenshot of a worked example

I understand this until the final two lines. How does he get from 27.8766 to 1149.8hz and 7224.7rad/s?


The answer to your first question comes from a little algebra. Subtract 7 from both sides, divide by 1.579e-5, and take the square root:

$$\sqrt{\frac{27.8766 - 7}{1.579\times10^{-5}}} = 1149.8$$

The conversion to radians per second is done by multiplying by \$2\pi\$ as they show.

To answer your follow up question about where \$1.579\times10^{-5}\$ comes from, it is equal to the expression from earlier in the same line, after factoring \$(2\pi f_{6dB})^2\$ into \$(2\pi)^2(f_{6dB})^2\$:


  • \$\begingroup\$ Thanks for the reply, I'm also a little confused as to where the 1.579x10^5 comes from? \$\endgroup\$ – James Apr 30 at 18:01
  • \$\begingroup\$ @James -- See edit \$\endgroup\$ – Justin Apr 30 at 18:05
  • 1
    \$\begingroup\$ @James I think your visual cortex might have missed the arrow in the middle of the third last line where it jumps to a whole new equation that does not equate to F(f_6db). It's a whole new inequality. I missed it too the first few times I looked at it. \$\endgroup\$ – DKNguyen Apr 30 at 18:28

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.