How to find fundamental frequency

In summary, when a 70kg aluminum sculpture is hung from a steel wire, the fundamental frequency for transverse standing waves is 250.0 Hz. When the sculpture is completely submerged in water, the new fundamental frequency can be calculated using the Archimedes principle and is directly proportional to the square root of the tension. The weight of the sculpture does not affect this calculation.
  • #1
ngcg
5
0

Homework Statement


When a 70kg aluminum (density = 2.7 g/cm3) sculpture is hung from a steel wire, the fundamental frequency for transverse standing waves on the wire is 250.0 Hz. The sculpture (but not the wire) is then completely submerged in water. What is the new fundamental frequency?


Homework Equations


f=ma
fundamental frequency = (1/2L)((Tensional force/linear density)^1/2)


The Attempt at a Solution


250=(1/2L)((686N/u)^1/2))
(stuck there)
 
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  • #2
According to the Archimedes principle, the loss of weight is equal to the weight of the displaced liquid. In the problem the liquid is the water whose density is 1 g/cm^3.
Hence when the sculpture is immersed in water, the new tension is
T' = mg - mg*ρ(w)/ρ(Al)
The frequency is directly proportional to the square root of the tension. Hence
f/f' = sqrt(T/T')
250/f' = sqrt[1/(1 - 1/2.7)]
Now solve for f'.
 
Last edited:
  • #3
so in this equation, the 70kg value does not matter?

by the way, thanks a lot! :)
 
  • #4
ngcg said:
so in this equation, the 70kg value does not matter?

by the way, thanks a lot! :)

Since we are taking the ratio of tensions, 70 kg does not matter.
 
  • #5
thank you!
 

1. What is fundamental frequency?

Fundamental frequency, also known as the first harmonic, is the lowest frequency produced by a vibrating object or sound source. It is the building block of all other frequencies in a sound and is essential for determining the pitch of a sound.

2. How do you find the fundamental frequency of a sound?

The fundamental frequency of a sound can be found by analyzing its waveform using a spectrum analyzer or by performing a Fast Fourier Transform (FFT) on the sound. Both methods will show the different frequencies present in the sound, with the fundamental frequency being the lowest and most prominent peak.

3. What factors affect the fundamental frequency of a sound?

The fundamental frequency of a sound can be affected by several factors, including the size and shape of the sound source, the tension and mass of the vibrating object, and the medium through which the sound is traveling. Additionally, the fundamental frequency can also be altered by the presence of harmonics and overtones.

4. How does the fundamental frequency relate to the pitch of a sound?

The fundamental frequency is closely related to the perceived pitch of a sound. Generally, the higher the fundamental frequency, the higher the pitch of the sound. However, the relationship between fundamental frequency and pitch can be complex, as other factors such as harmonics and overtones can also influence the perceived pitch of a sound.

5. Can the fundamental frequency of a sound be changed?

Yes, the fundamental frequency of a sound can be changed by altering the factors that affect it, such as the size and shape of the sound source or the tension and mass of the vibrating object. Additionally, applying filters or effects to a sound can also change its fundamental frequency and alter its perceived pitch.

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