What Is the Maximum EMF Induced in a Vibrating Guitar String? (2024)

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In summary: Using the given information, we can find the velocity of the section of wire in the magnetic field:v = \sqrt{\frac{F}{\mu \ell}}Where F is the force exerted on the wire, \mu is the linear density of the wire, and \ell is the length of the section of wire in the magnetic field. Plugging in the given values, we get:v = \sqrt{\frac{(301\ N)(1.50\ cm)}{(3.00\times10^{-3}\ kg/m)(2.00\ cm)}}Simplifying, we get v = 50 m/s. Now, since the wire is vibrating at its fundamental frequency, we can find the amplitude of

  • #1

Ithryndil

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Homework Statement

Review problem. A flexible metallic wire with linear density 3.00 multiplied by 10-3 kg/m is stretched between two fixed clamps 64.0 cm apart and held under tension 301 N. A magnet is placed near the wire as shown in Figure P31.25. Assume that the magnet produces a uniform field of 5.00 mT over a 2.00 cm length at the center of the wire and a negligible field elsewhere. The wire is set vibrating at its fundamental (lowest) frequency. The section of the wire in the magnetic field moves with a uniform amplitude of 1.50 cm.

http://www.webassign.net/serpop/p23-18.gif

(b) Find the amplitude of the electromotive force (emfmax) induced between the ends of the wire.

Homework Equations

Emf = BA

The Attempt at a Solution

I am not quite sure I am doing the problem correctly. I had the area being 3.00cm X 2.00cm but that's not correct nor do I actually believe the above equation is the correct equation. I assume the equation needs to have a sine or a cosine in it, but we are needing to find Emfmax so that's not too important right? Thanks for the help.

  • #2

Redbelly98

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Correction to your equation:

[tex]
Emf = \frac{d}{dt} (BA)
[/tex]

Since B is constant, the problem comes down to finding dA/dt.

  • #3

thomate1

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I would approach this problem by first understanding the physical principles involved. In this case, we have a wire moving in a magnetic field, which will induce an emf according to Faraday's law of induction. The equation you stated, Emf = BA, is actually the correct equation, where B is the magnetic field and A is the area of the wire perpendicular to the field.

To find the maximum emf, we need to consider the maximum area of the wire that is moving in the magnetic field. In this case, it is the section of the wire that is 2.00 cm long and has an amplitude of 1.50 cm. This gives us an area of 2.00 cm x 1.50 cm = 3.00 cm^2.

Now, we need to convert this to meters since the linear density and tension were given in SI units. 3.00 cm^2 is equivalent to 3.00 x 10^-4 m^2.

Finally, we can plug this into the equation Emf = BA, along with the given magnetic field of 5.00 mT, to get:

Emfmax = (5.00 x 10^-3 T)(3.00 x 10^-4 m^2) = 1.50 x 10^-6 V

Therefore, the maximum emf induced between the ends of the wire is 1.50 microvolts. I would also recommend double checking the units to make sure they are consistent throughout the calculation.

Related to What Is the Maximum EMF Induced in a Vibrating Guitar String?

1. What is "Emf max" for a guitar string?

Emf max refers to the maximum electromotive force or voltage that can be induced in a guitar string. This is typically measured in volts (V).

2. How is "Emf max" related to a guitar string's tension?

The emf max of a guitar string is directly proportional to its tension. This means that the higher the tension of the string, the higher the emf max will be.

3. Can the "Emf max" of a guitar string be changed?

Yes, the emf max of a guitar string can be changed by altering its tension, length, or material. Other factors like temperature and magnetic fields can also affect the emf max.

4. How does the "Emf max" of a guitar string affect the sound produced?

The emf max of a guitar string is directly related to the amplitude or loudness of the sound produced. A higher emf max will result in a louder sound, while a lower emf max will result in a softer sound.

5. Is the "Emf max" the same for all guitar strings?

No, the emf max can vary for different types of guitar strings. Steel strings, for example, have a higher emf max compared to nylon strings, which have a lower emf max. The emf max can also vary based on the thickness and length of the string.

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                      What Is the Maximum EMF Induced in a Vibrating Guitar String? (2024)

                      FAQs

                      What is the energy of a vibrating guitar string? ›

                      When the string is plucked, a certain amount of the potential energy is converted to kinetic energy. As the string vibrates, it is oscillating back and forth between the transfer of kinetic energy and potential energy. This is what gives the string resonance and a sustained sound.

                      What frequency do guitar strings vibrate at? ›

                      Low-E: 82 Hz (E2) A: 110 Hz (A2) D: 147 Hz (D3) G: 196 Hz (G3)

                      What is the frequency of the high E on a guitar? ›

                      246.94 Hz B (2nd string) 329.63 Hz High E (1st string)

                      How many Hz is low E on guitar? ›

                      The lowest note on the standard guitar is E at about 83 Hz, but a bass guitar can play down to 41 Hz. The orginary guitar can play notes with fundamental frequencies above 1 kHz. Human ears are most sensitive to sounds between 1 and 4 kHz - about two to four octaves above middle C.

                      What is the potential energy of vibrating string? ›

                      Potential energy, by definition, is the energy an object possesses due to its position relative to other objects. For a vibrating string, potential energy is primarily stored in the string when it's displaced from its equilibrium position, such as when a guitar string is plucked or drawn aside.

                      Is a vibrating guitar string an electromagnetic wave? ›

                      This is how a microwave oven heats up food. Option a, a vibrating guitar string, does produce a sound wave, but sound waves are mechanical waves, not electromagnetic waves.

                      What harmonic do guitar strings vibrate at? ›

                      Strings don't only vibrate at the first harmonic. The 1st harmonic is actually the fundamental frequency, which is determined by the string length, mass and tension. The fundamental is the most prominent vibration but a vibrating string also contains 2nd, 3rd, 4th, etc …. order harmonics as well.

                      What wave is produced in vibrations in A guitar string? ›

                      Hence, the waves that are produced in the string of a guitar are Transverse waves. Q. The pitch of the sound produced by a guitar can be altered by reducing the vibrating length of the guitar string.

                      What waves are produced on A vibrating guitar string? ›

                      Plucking a guitar string is an example of transverse wave of string vibration as it sets up up and down vibrations of the string, while sound produced by it gives you a longitudinal wave in the air because of compression and rarefaction of molecules produced in the air.

                      What are the frequencies of the E and A string of A guitar? ›

                      Here are the frequencies you'll tune to for E Standard: 82.41 Hz Low E (6th string) 110.00 Hz A (5th string) 146.83 Hz D (4th string)

                      What guitar tuning is 432 Hz? ›

                      A=432Hz—also known as “Verdi's A,” after composer Giuseppe Verdi, who preferred the 432 standard—is said by advocates to be in tune with the laws of nature and mathematically consistent with the universe.

                      What is the best frequency for A guitar? ›

                      Most players agree that the midrange is the most important frequency zone for guitar.
                      • But this area is a broad range that begins at 300Hz and extends up to 5kHz. ...
                      • For example, boosting midrange frequencies around 300-800Hz adds a sense of fatness that many associate with vintage guitar tones.
                      Dec 7, 2022

                      What Hz is drop-D tuning? ›

                      Special Note: If you use a drop-D tuning (the 6th string tuned down to D, the open D is 73 Hz and D# at the 1st fret is 78 Hz.

                      What is the lowest guitar E? ›

                      On the most common, 6-string guitar with standard tuning (EBGDAE) the lowest note is E, or to be more specific it's E3 (E note in 3rd octave). The lowest note on 6-string guitar with Drop-D tuning (EBGDAD) is D (D3).

                      Which is high E and low E on guitar? ›

                      Finding guitar string notes: EADgbe

                      To help memorize these string names, there are a couple of sayings that we can use: Eddie Ate Dynamite, Good Bye Eddie or Eat A Dead Grasshopper Before Everything. The 1st string is the high E and the low string is the 6th string.

                      What type of wave is a vibrating guitar string? ›

                      Plucking a guitar string is an example of transverse wave of string vibration, while sound produced by it gives you a longitudinal wave in the air.

                      What is the energy of the guitar? ›

                      What type of energy does a guitar use? Acoustical guitars use mechanical energy, transfered from your plucking fingers or pick, to the vibrating string, to the resonant top of the instrument, and to the vibrating air in the body of the guitar.

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