How do you find the mass of a vibrating metal wire on a piano?

In summary, the conversation discusses finding the total mass of a piano wire based on its length, tension, and fundamental frequency. The relevant equations are v = √(FL/m) and linear mass density equations. The solution involved manipulating the equation m = FL/v^2 and using the velocity of sound. The conversation ends with the person finding the equation and the answer.
  • #1
bobby3280
12
0

Homework Statement



The longest "string" (a thick metal wire) on a particular piano is 3.0 m long and has a tension of 300.0 N. It vibrates with a fundamental frequency of 27.4 Hz. What is the total mass of the wire? ( in kg)

Homework Equations



The only relevant equation I could find is v = square root of ( FL / m )
or the linear mass density equations

The Attempt at a Solution



I move m to one side leaving m = FL / v^2 and tried velocity of sound 343 m/s but no luck.

This seems to be the only viable equation to me and I either don't know how to convert 27.4 Hz to velocity or am completely lost.

Thanks for any help
 
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  • #2
What equations do you have for the frequency of a string under tension?
 
  • #3
Thanks found the equation and answer.
 

FAQ: How do you find the mass of a vibrating metal wire on a piano?

What is the relationship between wave frequency and mass?

The relationship between wave frequency and mass is an inverse one. This means that as the mass of an object increases, the frequency of its waves decreases. Similarly, as the mass decreases, the frequency increases. This relationship is known as the mass-spring system, where a heavier object will take longer to complete one full wave cycle compared to a lighter object.

How does the frequency of a wave affect its energy?

The frequency of a wave directly affects its energy. Higher frequency waves have more energy, while lower frequency waves have less energy. This is because higher frequency waves have more cycles per second, meaning they are able to transfer more energy in a given amount of time.

Can mass affect the speed of a wave?

No, the mass of an object does not affect the speed of a wave. The speed of a wave is determined by the medium it is traveling through, not the mass of the object creating the wave. However, the frequency and wavelength of a wave can be affected by the mass of the object.

How can you calculate the frequency of a wave?

The frequency of a wave can be calculated by dividing the velocity of the wave by its wavelength. The formula for frequency is f = v/λ, where f is frequency, v is velocity, and λ is wavelength.

What is the difference between amplitude and frequency?

Amplitude and frequency are two different properties of a wave. Amplitude is the measure of the maximum displacement of a wave from its rest position, while frequency is the number of cycles of a wave that occur in one second. Amplitude is measured in units of distance, while frequency is measured in units of hertz (Hz).

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