Order of Operations: Guitar String Frequency

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In summary, the conversation discusses a problem involving a guitar string of a certain length and tension producing a specific frequency. It then presents a different scenario with a change in tension and length, and asks for the resulting frequency. The conversation also includes an attempt at solving the problem, but requests clarification on the order of operations. The expert suggests providing more information and relevant equations in order to properly address the question.
  • #1
Spookie71
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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
[tex]f_{f}[/tex] = 330 Hz * [tex]\sqrt{ \frac{100.0 N}{81.0 N}}[/tex] * [tex]\frac{30.0 cm}{25.0 cm}[/tex]

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
 
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  • #2
Write down the eqn giving frequency in terms of length, tension etc.
 
  • #3
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
 
  • #4
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.
 

What is the order of operations for calculating guitar string frequency?

The order of operations for calculating guitar string frequency is as follows:

  1. Start by determining the length of the string (L), measured in meters.
  2. Next, find the tension of the string (T), measured in Newtons.
  3. Then, calculate the mass per unit length of the string (μ), measured in kilograms per meter.
  4. Use the equation f = 1/2L * √(T/μ) to find the frequency (f) of the string, measured in Hertz (Hz).

What is the significance of each variable in the frequency equation?

The variables used in the frequency equation have specific meanings:

  • L (length): This is the distance between the two fixed points where the string is attached.
  • T (tension): This is the force pulling on the string, created by tuning the guitar.
  • μ (mass per unit length): This is the mass of the string per unit of its length, which is affected by the material and thickness of the string.
  • f (frequency): This is the number of cycles per second that the string vibrates at, which determines the pitch of the note produced.

How does changing the length or tension of a guitar string affect its frequency?

Changing the length or tension of a guitar string can greatly impact its frequency:

  • Length: Shorter strings produce higher frequencies, resulting in a higher pitch, while longer strings produce lower frequencies and a lower pitch.
  • Tension: Higher tension on a string will increase its frequency and pitch, while lower tension will decrease frequency and pitch.

What factors can affect the accuracy of guitar string frequency calculations?

There are several factors that can affect the accuracy of guitar string frequency calculations:

  • Material: The density and elasticity of the string material can alter its mass and tension, affecting the frequency.
  • Temperature: Changes in temperature can cause the string to expand or contract, altering its length and tension.
  • Humidity: Moisture in the air can also affect the tension and mass of the string, resulting in changes to the frequency.
  • Human error: Accurate measurements and calculations are crucial for precise frequency calculations, so any errors during these steps can affect the final result.

How is the order of operations for guitar string frequency related to other scientific principles?

The order of operations for calculating guitar string frequency is related to several other scientific principles, including:

  • Harmonic motion: The vibration of a guitar string follows the principles of harmonic motion, where the string's motion is periodic and can be represented by a sine wave.
  • Newton's laws of motion: The tension on a guitar string is created by the force applied when tuning, and follows Newton's third law of motion - for every action, there is an equal and opposite reaction.
  • Sound waves: The frequency of a guitar string determines the pitch of the note produced, and sound waves are created by vibrations at specific frequencies.

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