Fundamental frequency and tension

In summary, the conversation discusses finding the required tension for a guitar string when its fundamental frequency is changed. The equations v = sqrt(T/u) and f1 = v/2L are used to calculate the tension and speed of the string, and the frequency ratio f2/f1 is used to solve for the unknown variables. The conversation concludes with the answer being obtained.
  • #1
k77i
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0

Homework Statement



A guitar string has a fundamental frequency of 429 Hz when its tension is 259 N.
The string is being tuned to a fundamental frequency of 388 Hz. What is the required tension?

Homework Equations



v = sqrt(T/u): where v is the speed, T is the tension and u is the linear mass density
f1 = v/2L: where f1 is the fundamental frequency, v is the speed again and L the length of the string

The Attempt at a Solution



sqrt(T/u) = f1(2L)
sqrt(259/u) = 858L

I tried to use the speed equations to find u or L, which would allow me to calculate the v after and then get the frequency, but I'm still left with 2 unknowns. Am I using the wrong equations to solve this?
 
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  • #2
You have two equations, one for f1=429Hz and one for f2=259Hz
Write each one as f=v/2L and substitute for v in terms of T and u
Then do f2/f1=
 
  • #3
Oh I get it now. It should have been obvious but I was just having trouble with cancelling out the unknown terms. Thanks I managed to get the answer.
 

FAQ: Fundamental frequency and tension

What is fundamental frequency?

Fundamental frequency, also known as the first harmonic, is the lowest frequency at which a system or object can vibrate and produce a sound. It is the basis for all other frequencies and determines the perceived pitch of a sound.

How is fundamental frequency related to tension?

There is a direct relationship between fundamental frequency and tension. As tension increases, the fundamental frequency also increases. This is because a higher tension causes the system or object to vibrate at a faster rate, producing a higher frequency sound.

What factors affect the fundamental frequency of a vibrating object?

The fundamental frequency of a vibrating object is affected by several factors, including the length, mass, and tension of the object. The material and temperature of the object can also have an impact on its fundamental frequency.

Why is fundamental frequency important?

Fundamental frequency is important because it is the basis for all other frequencies in a sound. It helps determine the perceived pitch of a sound and is essential in music and speech production. Understanding fundamental frequency also allows scientists to study the properties of different materials and systems.

How is fundamental frequency measured?

Fundamental frequency is typically measured in Hertz (Hz), which is the unit for frequency. It can be measured using a variety of instruments, such as a tuning fork, oscilloscope, or frequency analyzer. The frequency can also be calculated using mathematical formulas based on the properties of the vibrating object.

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