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Wire Vibration
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⚡ Quick Summary
The frequency of a vibrating wire depends on its length and tension. Changing the length or tension will change the frequency.
f ∝ √(T)/L, where f is frequency, T is tension, and L is length.
The fundamental frequency of a vibrating wire is directly proportional to the square root of the tension and inversely proportional to the length of the wire. If the tension is increased, the frequency increases, and if the length is increased, the frequency decreases. The number of beats produced per second is the difference in frequency between the vibrating wire and the tuning fork.
Tuning Forks and Beats
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The beat frequency helps determine the unknown frequency of a tuning fork by comparing it to a known frequency and observing how the beat frequency changes when the tuning fork is slightly altered.
Beat frequency = |f1 - f2|, where f1 and f2 are the frequencies of the two tuning forks.
If loading a tuning fork (e.g., with wax) decreases its frequency, and this *decreases* the beat frequency relative to a known fork, then the original unknown frequency was *higher* than the known. Conversely, if loading decreases the tuning fork frequency, and this *increases* the beat frequency, then the original unknown frequency was *lower* than the known. This allows solving for the precise original frequency.
Frequency and Wavelength
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The speed of a wave is related to its frequency and wavelength.
v = f * lambda, where v is the speed of the wave, f is the frequency, and lambda is the wavelength.
The speed of a wave in a medium is related to the frequency and wavelength of the wave. Higher frequency waves have shorter wavelengths, and lower frequency waves have longer wavelengths, for a given speed.
Beats
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Beats are produced when two sound waves of slightly different frequencies interfere. The beat frequency is the difference between the two frequencies.
Beat frequency = |f1 - f2|, where f1 and f2 are the frequencies of the two sound waves.
When two sound waves with slightly different frequencies are played simultaneously, the resulting sound has a varying amplitude, creating a periodic variation in loudness called beats. The number of beats per second equals the difference in the frequencies of the two sound waves.
Kundt's Tube
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A Kundt's tube is used to measure the speed of sound in a solid. It relies on creating standing waves in both the solid and the air within the tube.
v = f * lambda, where v is the speed of sound, f is the frequency, and lambda is the wavelength (twice the distance between nodes).
Kundt's tube demonstrates resonance in a solid rod and the air within a tube. The solid rod is vibrated, producing sound waves in the air. The powder in the tube collects at the nodes of the standing wave pattern. By measuring the distance between the nodes and knowing the frequency, one can calculate the speed of sound in both the air and the solid rod.
Fundamental Frequency of Closed Pipe
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The fundamental frequency of a closed pipe is the lowest frequency at which it resonates. It depends on the length of the pipe and the speed of sound.
f = v / (4L), where f is the fundamental frequency, v is the speed of sound, and L is the length of the pipe.
A closed pipe (closed at one end) supports standing waves with a node at the closed end and an antinode at the open end. The fundamental frequency corresponds to a quarter-wavelength fitting inside the pipe length.
Doppler Effect
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The Doppler effect describes the change in frequency of a sound wave perceived by an observer when the source of the sound and the observer are in relative motion.
Observed frequency f' = f (v + vo) / (v - vs), where f is the source frequency, v is the speed of sound, vo is the observer's velocity (positive if approaching source), and vs is the source velocity (positive if approaching observer).
The Doppler effect occurs when a source of waves is moving relative to an observer. If the source is approaching, the observed frequency is higher than the emitted frequency. If the source is receding, the observed frequency is lower. The change in frequency depends on the speeds of the source and observer relative to the medium (air, in this case) carrying the sound.
SI
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The International System of Units.
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The International System of Units (SI) is the modern form of the metric system and is the most widely used system of measurement.
CGS
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Centimeter-Gram-Second system of units.
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The CGS (centimeter-gram-second) system is a system of units based on the centimeter, gram, and second as the base units of length, mass, and time, respectively.
Units
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Standard quantities used to express measurements.
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Units are standard quantities used to express measurements. They provide a common reference for comparing different quantities.
Significant Digits
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The digits in a number that are known with certainty plus one uncertain digit.
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Significant digits are the digits in a number that are known with certainty plus one uncertain digit. They are used to indicate the precision of a measurement.
Young's Double-Slit Experiment
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An experiment demonstrating the wave nature of light.
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Young's double-slit experiment is a classic experiment that demonstrates the wave nature of light. When light passes through two narrow slits, it produces an interference pattern on a screen behind the slits.
Total Internal Reflection
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The phenomenon when light is reflected back into the medium instead of being refracted.
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Total internal reflection is the phenomenon that occurs when a ray of light strikes the boundary between two media and is reflected back into the first medium instead of being refracted into the second medium. It occurs when light travels from a medium with a higher refractive index to a medium with a lower refractive index at an angle of incidence greater than the critical angle.
Snell's Law
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Law describing the relationship between angles of incidence and refraction.
n₁sinθ₁ = n₂sinθ₂
Snell's law (also known as the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.
Telescope
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An optical instrument used to view distant objects.
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A telescope is an optical instrument used to view distant objects by collecting and focusing electromagnetic radiation.
Quality
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The timbre or tone color of a sound.
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Quality (or timbre) is the characteristic that distinguishes sounds with the same pitch and loudness. It depends on the combination of harmonics present in the sound.
Pitch
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The perceived frequency of a sound.
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Pitch is the perceived frequency of a sound, which determines how high or low it sounds to the human ear.
Loudness
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A subjective measure of the intensity of sound.
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Loudness is a subjective measure of the intensity of sound as perceived by the human ear. It depends on both the intensity and frequency of the sound.
Ultrasonic
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Sound waves with frequencies above the human hearing range.
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Ultrasonic waves are sound waves with frequencies above the human hearing range (typically above 20 kHz).
Infrasonic
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Sound waves with frequencies below the human hearing range.
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Infrasonic waves are sound waves with frequencies below the human hearing range (typically below 20 Hz).