What is the Tension of a Cello String with Given Frequency and Linear Density?

In summary, the conversation discusses finding the tension of a cello string with a linear density of m/L = 1.56 x 10^-2 kg/m, producing a frequency of 65.4 Hz and having a length of .800 m. The equations v= sqrt(F/(m/L)) and v= f (lambda) are suggested, but it is determined that the length given is actually half the wavelength for the fundamental mode, so λ = 2L. This information helps to find the correct velocity and ultimately the tension of the string.
  • #1
RaPiD
15
0

Homework Statement



On a cello, the string has (linear density) m/L = 1.56 x 10^-2 kg/m, and produces frequency of 65.4 Hz and has length of .800 m between the fixed ends. Find the tension.

Homework Equations



v= sqrt(F/(m/L))

v= f (lambda)

The Attempt at a Solution



I first thought to find the velocity first, then plug in the velocity into the first equation and then find the tension. But, then I figured that the length given was the length of the string and not the wavelength so that eliminates using the second equation. Is there another equation to use, that's not occurring to me to find the velocity?
 
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  • #2
Your equatoins are correct, but the length of the string is half the wavelength for the fundamental mode, so λ = 2L.
 
  • #3
thanks dx that clears up a lot
 
  • #4
No problem. Welcome to PF.
 

FAQ: What is the Tension of a Cello String with Given Frequency and Linear Density?

1. What are waves on a cello string?

Waves on a cello string refer to the vibrations that occur when a cello string is plucked or bowed. These vibrations travel through the string and produce sound.

2. How do waves on a cello string produce sound?

When the cello string is plucked or bowed, it creates waves that travel through the string. These waves cause the string to vibrate at a specific frequency, which produces sound waves that travel through the air and reach our ears.

3. What factors affect the waves on a cello string?

The waves on a cello string can be affected by various factors such as the tension and thickness of the string, the length of the string, and the material it is made of. These factors can impact the frequency and amplitude of the waves, thus affecting the sound produced.

4. How are waves on a cello string different from other types of waves?

Waves on a cello string are mechanical waves, meaning they require a medium (the string) to travel through. They also have a specific frequency and amplitude, unlike other types of waves such as electromagnetic waves.

5. Can waves on a cello string be manipulated to produce different sounds?

Yes, the waves on a cello string can be manipulated by changing the tension, thickness, or length of the string. This results in different frequencies and amplitudes, producing different sounds. Additionally, different playing techniques such as plucking or bowing can also affect the waves and produce different sounds.

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