Order of Operations: Guitar String Frequency

[Spookie71]

Homework Statement

A guitar string of length 60.0 cm under 81.0 N of tension produces a note of frequency 330.0 Hz. What frequency will the same string produce when under 100.0 N of tension and shortened to 25.0 cm?

Homework Equations

Here is the question
f_{f} = 330 Hz * \sqrt{ \frac{100.0 N}{81.0 N}} * \frac{30.0 cm}{25.0 cm}

The answer is 417.42 Hz in the book, I just don't know the order of operations to solve this.

The Attempt at a Solution

When I try it I take 100.0 N and divide by 81.0 N where I get 1.234567901 and then I push the square root key on my calculator which gives me 1.111111111

I then take 330 * by 1.111111111 * 1.2

Which gives me 440 Hz.

Can you explain where I'm going wrong in my order of operations.

Thanks

 

[Shooting Star]

Write down the eqn giving frequency in terms of length, tension etc.

 

[Spookie71]

Shooting star:

Not sure what you're saying.

I apoligize for my lack of knowlegdge. I'm returning to school to complete my diploma after being out for 15 years. I picked a course that may be a little to advanced for me but I don't want to lose the money I put down for it.

Do you need more information from me as per the equation?

Thanks
S

 

[Shooting Star]

Actually, I don't know under what topic you're doing this problem. Is it under sound and waves etc or just ratio-proportion or scaling? But the fact remains that unless you give more information about why you're doing what you're doing, with relevant equations, your questions are not possible to reply to. So, for your benefit, I suggest you give more details and write the pertinent equations on the topic. Best wishes.