Forced Vibration in Sound and Guitar
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Questions and Answers

What is the intensity ratio when the decibel level increases from 40 dB to 100 dB?

  • $10^6$ (correct)
  • $10^2$
  • $10^8$
  • $10^4$

    • If one machine in a factory operates at 80 dB, how many identical machines can be added without exceeding a limit of 90 dB?

  • 11
  • 9 (correct)
  • 10
  • 1

    • Which equation correctly describes the relationship between the number of machines and their decibel levels to maintain compliance with federal regulations?

  • $N_T = N_{given} - 10^{(B_T - B) / 10}$
  • $N_T = N_{given} imes 10^{(B_T - B) / 10}$
  • $N_T = N_{given} / 10^{(B_T - B) / 10}$
  • $N_T = N_{given} + 10^{(B_T - B) / 10}$ (correct)

    • What does a negative power in intensity indicate?

    <p>Decrease in intensity</p> Signup and view all the answers

    When calculating the intensity ratio for a 50 dB to 70 dB increase, what is the resulting value?

    <p>$10^2$</p> Signup and view all the answers

    What primarily causes forced vibration in an object?

    <p>External force applied to the object</p> Signup and view all the answers

    What happens to a string on a guitar when it is plucked while being attached to the guitar body?

    <p>It vibrates and transfers energy to the guitar body</p> Signup and view all the answers

    Why do strings vibrate more efficiently when attached to the bridge of the guitar?

    <p>The bridge has a larger surface area</p> Signup and view all the answers

    What is a key characteristic of the sound produced by a vibrating guitar string when not attached to the body?

    <p>Very low sound intensity</p> Signup and view all the answers

    What role does the guitar body play in sound amplification when strings vibrate?

    <p>It enhances the exchange of sound energy between the strings and air</p> Signup and view all the answers

    What is a consequence of the forced vibrations in a guitar?

    <p>Sound intensity is increased due to energy transfer</p> Signup and view all the answers

    What happens to the sound intensity when a string is plucked while resting on a surface, compared to being isolated?

    <p>Sound intensity increases due to resonance</p> Signup and view all the answers

    Why do vibrations from the strings die out faster when attached to the guitar body?

    <p>The energy is efficiently transferred to the air</p> Signup and view all the answers

    What is the defining characteristic of resonance in a system?

    <p>The frequency of force applied matches the natural frequency of the system.</p> Signup and view all the answers

    Which of the following statements is true regarding properties of resonance vibrations?

    <p>Resonance can lead to structural damage due to high amplitudes.</p> Signup and view all the answers

    In the context of forced vibrations, what does the equation $f_{force} = f_{natural}$ signify?

    <p>An amplification of the system's response occurs.</p> Signup and view all the answers

    Which scenario illustrates the risks associated with resonance in structures?

    <p>The collapse of the Washington bridge due to specific vibrations.</p> Signup and view all the answers

    Which principle best describes why resonance can lead to failures in mechanical systems?

    <p>Natural frequencies can match with external forces leading to increased energies.</p> Signup and view all the answers

    What triggered the collapse of the Tacoma Narrows Bridge in 1940?

    <p>High winds generating standing waves</p> Signup and view all the answers

    During the Loma Prieta earthquake, what specific frequency contributed to the freeway collapse?

    <p>1.5 Hz, close to the natural frequency of the roadway</p> Signup and view all the answers

    In the context of resonance, what is the significance of a driving frequency being close to the natural frequency of a structure?

    <p>It leads to increased amplitude and potential structural failure.</p> Signup and view all the answers

    What is a key characteristic of the movement of the Tacoma Narrows Bridge that led to its failure?

    <p>Oscillation at its natural frequency due to external forces</p> Signup and view all the answers

    Which phenomenon is illustrated by the different amplitudes of vibration in the simple pendulum?

    <p>The concept of resonance when driven at a close frequency</p> Signup and view all the answers

    What is the relationship between sound intensity and distance from the sound source?

    <p>Sound intensity is inversely proportional to the distance squared.</p> Signup and view all the answers

    Which equation is used to find the intensity of sound?

    <p>$I = rac{P}{A}$</p> Signup and view all the answers

    What happens to sound intensity if the energy output of the sound source increases?

    <p>Sound intensity increases.</p> Signup and view all the answers

    Which of the following statements about sound intensity is true?

    <p>Sound intensity decreases with increased distance from the source.</p> Signup and view all the answers

    Using which formula can the power of a sound wave be calculated?

    <p>$P = 4πr^2 imes I$</p> Signup and view all the answers

    What does the equation $I_2/I_1 = r_1^2/r_2^2$ represent?

    <p>Relationship between intensities and distances of sound waves.</p> Signup and view all the answers

    If the area of the wave front is doubled while keeping the power constant, what happens to the intensity?

    <p>Intensity halves.</p> Signup and view all the answers

    Which factor does NOT affect the intensity of sound waves?

    <p>Humidity of the air.</p> Signup and view all the answers

    What is the definition of relative intensity in the context of sound waves?

    <p>The ratio of the intensity of a given sound wave to the intensity at the threshold of hearing.</p> Signup and view all the answers

    Why is the decibel level considered dimensionless?

    <p>It is proportional to the logarithm of a ratio of two intensities.</p> Signup and view all the answers

    If the threshold of pain intensity is given as $I = 1.0 W/m^2$, what is the decibel level at this threshold?

    <p>120 dB</p> Signup and view all the answers

    What is the mathematical representation of determining the lowest decibel level (threshold of hearing)?

    <p>$B_{lowest} = 10\log \frac{I_0}{I_0}$</p> Signup and view all the answers

    Which of the following statements about the bel and decibel is correct?

    <p>1 bel is equal to 10 decibels.</p> Signup and view all the answers

    What occurs when a force is removed from an object that is undergoing forced vibration?

    <p>The object stops vibrating completely.</p> Signup and view all the answers

    Which statement best describes the relationship between the amplitude of resonance and the natural frequency of a pendulum?

    <p>Resonance increases amplitude only if the frequencies are the same.</p> Signup and view all the answers

    What is the main reason sound intensity increases when a guitar string is placed on a guitar?

    <p>The guitar body resonates with the string's frequency.</p> Signup and view all the answers

    Which factor does NOT affect the natural frequency of a simple pendulum?

    <p>Mass of the pendulum</p> Signup and view all the answers

    Which property is true for forced vibrations?

    <p>They require an external force to occur.</p> Signup and view all the answers

    How does the energy transfer in a system of pendulums when one is set in motion?

    <p>Energy transfers from one pendulum, increasing the amplitude of another.</p> Signup and view all the answers

    What is a key characteristic of natural vibrations?

    <p>They occur without any force being applied.</p> Signup and view all the answers

    What happens to the amplitude of the pendulum that is not in resonance when another pendulum of matching frequency is excited?

    <p>Its amplitude decreases.</p> Signup and view all the answers

    Which statement best describes the response of an isolated string when plucked?

    <p>It hardly produces sound due to low energy transfer.</p> Signup and view all the answers

    What is the role of the guitar body when a string is plucked?

    <p>To match frequencies and amplify vibrations.</p> Signup and view all the answers

    What is the threshold of hearing for the average human ear?

    <p>$1.0 imes 10^{-12} W/m^2$</p> Signup and view all the answers

    At what intensity does sound begin to cause pain in the human ear?

    <p>$1.0 W/m^2$</p> Signup and view all the answers

    Which frequency range requires higher intensity levels to be audible?

    <p>Below 50 Hz and above 12000 Hz</p> Signup and view all the answers

    Why might prolonged exposure to sounds below the threshold of pain still damage hearing?

    <p>They can still vibrate the ear at damaging levels.</p> Signup and view all the answers

    Why do musicians wear earplugs during performances?

    <p>To protect against damage from high intensities and prolonged exposure to lower intensities.</p> Signup and view all the answers

    Study Notes

    Forced Vibration

    • Forced vibration occurs when an external force acts on an object, causing it to vibrate without aligning with its natural frequency.
    • When the external force is removed, the object ceases to vibrate, resulting in a loud sound perceived by the ear.
    • Key properties include exertion of force, lack of natural frequency, short duration of vibration post-force, and high energy reaching the ear.

    Guitar Example

    • An isolated guitar string produces minimal sound when plucked due to vibrating at its natural frequency, emitting little energy.
    • When the string is on a guitar, it engages in forced vibration, amplifying sound intensity through the resonance with the guitar body.
    • The bridge transfers vibrations to the guitar body, which has a larger surface area, enhancing sound energy transfer to the air.

    Sound Wave and Intensity

    • Sound intensity measures the energy flow rate through a specific area, defined by equations that relate intensity (I), power (P), and area (A).
    • Intensity equations include (I = \frac{P}{A}) and variations to calculate parameters based on known values.
    • Sound intensity depends on sound energy per time, area squared, and inversely on the distance from the source.

    Decibel Level Calculations

    • Decibel levels assess relative intensity compared to the threshold of hearing, described with the formula (B=10 \log\frac{I}{I_0}).
    • An example shows that when decibel levels rise (e.g., from 40 to 60 dB), intensity increases significantly, with the intensity ratio calculated.
    • Intensity adjustments reflect changes in sound sources, guiding compliance with federal regulations on noise levels.

    Resonance

    • Resonance occurs when the applied force frequency matches the object's natural frequency, amplifying vibrations with potentially destructive amplitudes.
    • Structural resonance can lead to failures like the Tacoma Narrows Bridge collapse, triggered by wind-induced vibrations matching natural frequencies.

    Natural Vibrations vs. Forced Vibrations

    • Natural vibrations require no external force and emit less energy while vibrating at a specific frequency dependent on factors like length or material.
    • Forced vibrations involve energy input from external forces, resulting in sudden, often louder sound emissions.

    Intensity and Frequency

    • The audible range for the human ear is dictated by both intensity and frequency, with low or high frequencies requiring greater intensity to be perceived.
    • Thresholds of hearing and pain define the audible limits, with levels established at (1.0 \times 10^{-12} W/m^2) and (1.0 W/m^2), respectively.
    • Extended exposure to sounds above the pain threshold can cause ear damage, prompting musicians to use ear protection during performances.

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    Description

    Explore the concept of forced vibration and its impact on sound intensity, particularly in the context of guitar strings. Understand how external forces influence vibrations and how the guitar amplifies sound through resonance. Learn about the properties and characteristics of sound waves in this insightful quiz.

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