Physics
Period, Frequency and Amplitude
Period, frequency, and amplitude are fundamental concepts in the study of waves and oscillations. The period refers to the time it takes for a wave to complete one full cycle, while frequency measures the number of cycles per unit of time. Amplitude, on the other hand, represents the maximum displacement of a wave from its equilibrium position.
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10 Key excerpts on "Period, Frequency and Amplitude"
eBook - PDF- Stanley A. Gelfand, Lauren Calandruccio(Authors)
- 2022(Publication Date)
- Thieme(Publisher)
● 1/500 = 0.002 and 1/0.002 = 500. ● 1/1000 = 0.001 and 1/0.001 = 1000. In each case, the period corresponds to 1 over the frequency, and the frequency corresponds to 1 over the period. In formal terms, frequency equals the re- ciprocal of period, and period equals the reciprocal of frequency, f ¼ 1 t Fig. 1.9 Each frame shows two sine waves that have the same frequency but different amplitudes. Compared with the upper frame, twice as many cycles occur in the same amount of time in the lower frame; thus, the period is half as long and the frequency is twice as high. 1 Acoustics and Sound Measurement 13 Each wave in the upper frame of Fig. 1.9 contains two cycles in 4 milliseconds, and each wave in the lower frame contains four cycles in the 4 millisec- onds. If two cycles in the upper frame last 4 millisec- onds, then the duration of one cycle is 2 milliseconds. Hence, the period of each wave in the upper frame is 2 milliseconds (t = 0.002 s), and the frequency is 1/0.002, or 500 Hz. Similarly, if four cycles last 4 milliseconds in the lower frame, then one cycle has a period of 1 millisecond (t = 0.001 s), and the frequency is 1/0.001, or 1000 Hz. Fig. 1.9 also illustrates differences in the ampli- tude between waves. Amplitude denotes size or magnitude, such as the amount of displacement, power, pressure, etc. The larger the amplitude at some point along the horizontal (time) axis, the greater its distance from zero on the vertical axis. With respect to the figure, each frame shows one wave that has a smaller amplitude and an other- wise identical wave that has a larger amplitude. As illustrated in Fig. 1.10, the peak-to-peak amplitude of a wave is the total vertical distance between its negative and positive peaks, and peak amplitude is the distance from the baseline to one peak. However, neither of these values reflects the overall, ongoing size of the wave because the ampli- tude is constantly changing.
eBook - PDF- Stanley A. Gelfand(Author)
- 2011(Publication Date)
- Thieme(Publisher)
Hence, the period of each wave in the upper frame is 2 milliseconds (t = 0.002 sec), and the frequency is 1/0.002, or 500 Hz. Similarly, if four cycles last 4 milliseconds in the lower frame, then one cycle has a period of 1 millisecond (t = 0.001 sec), and the frequency is 1/0.001, or 1000 Hz. Fig. 1.8 also illustrates differences in the am-plitude between waves. Amplitude denotes size or magnitude, such as the amount of its dis-placement, power, pressure, etc. The larger the amplitude at some point along the horizontal (time) axis, the greater its distance from zero on the vertical axis. With respect to the figure, each frame shows one wave that has a smaller ampli-tude and an otherwise identical wave that has a larger amplitude. As illustrated in Fig. 1.9 , the peak-to-peak amplitude of a wave is the total vertical distance between its negative and positive peaks, and peak amplitude is the distance from the base-line to one peak. However, neither of these val-ues reflects the overall, ongoing size of the wave because the amplitude is constantly changing. At any instant an oscillating particle may be at its most positive or most negative displacement from the resting position, or anywhere between these two extremes, including the resting posi-tion itself, where the displacement is zero. The magnitude of a sound at a given instant ( instan-taneous amplitude ) is true only for that mo-ment and will be different at the next moment. Yet we are usually interested in a kind of “overall average” amplitude that reveals the magnitude of a sound wave throughout its cycles. A simple average of the positive and negative instanta-neous amplitudes will not work because it will always be equal to zero. A different kind of over-all measure is therefore used, called the root-mean-square (RMS) amplitude.
eBook - PDF- Stanley A. Gelfand(Author)
- 2016(Publication Date)
- Thieme(Publisher)
1.9 contains two cycles in 4 milliseconds, and each wave in the lower frame contains four cycles in the 4 millisec-onds. If two cycles in the upper frame last 4 millisec-onds, then the duration of one cycle is 2 milliseconds. Hence, the period of each wave in the upper frame is 2 milliseconds (t = 0.002 second), and the frequency is 1/0.002, or 500 Hz. Similarly, if four cycles last 4 milliseconds in the lower frame, then one cycle has a period of 1 millisecond (t = 0.001), and the fre-quency is 1/0.001, or 1000 Hz. Fig. 1.9 also illustrates differences in the ampli -tude between waves. Amplitude denotes size or magnitude, such as the amount of displacement, power, pressure, etc. The larger the amplitude at some point along the horizontal (time) axis, the greater its distance from zero on the vertical axis. With respect to the figure, each frame shows one wave that has a smaller amplitude and an otherwise identical wave that has a larger amplitude. As illustrated in Fig. 1.10 , the peak-to-peak amplitude of a wave is the total vertical distance between its negative and positive peaks, and peak amplitude is the distance from the baseline to one peak. However, neither of these values reflects the overall, ongoing size of the wave because the ampli-tude is constantly changing. At any instant an oscil-lating particle may be at its most positive or most negative displacement from the resting position, or anywhere between these two extremes, including Amplitude Amplitude 0 1 2 Time (msec) 3 4 0 1 2 Time (msec) 3 4 Fig. 1.9 Each frame shows two sine waves that have the same frequency but different amplitudes. Compared with the upper frame, twice as many cycles occur in the same amount of time in the lower frame; thus the period is half as long and the frequency is twice as high. 0.707 +1 –1 Root mean square (RMS) amplitude is 0.707 of peak amplitude. 0.707 Amplitude RMS Peak-to-peak Peak Fig. 1.10 Peak, peak-to-peak, and root-mean-square (RMS) amplitude.
eBook - PDFWaves and Oscillations in Nature
An Introduction
- A Satya Narayanan, Swapan K Saha(Authors)
- 2015(Publication Date)
- CRC Press(Publisher)
The incident idealized photon is monochromatic in nature. The corresponding classical wave has the same extent as well. For a wave traveling through a medium, a crest is seen moving along from particle to particle. This crest is followed by a trough which, in turn, is followed by the next crest. A distinct wave pattern in the form of a sine wave is observed traveling through the medium. This sine wave pattern continues to move in uninterrupted fashion until it encounters another wave along the medium or until it encounters a boundary with another medium. This type of wave pattern is referred to as a traveling wave; for instance, an ocean wave is falling under such category. The wave properties that are described by the following quantities are interrelated. 1. Amplitude: The amplitude of a wave is the maximum displacement of a particle from its equilibrium position as the wave passes through it (see Figure 1.3). It is measured in meters (m). amplitude y x λ FIGURE 1.3 : Amplitude pattern. 2. Frequency: The number of cycles per unit of time is called the frequency, ν , of oscillations caused by the wave. The unit of frequency is hertz (Hz; cycles per second). The quantity ν = ω 2 π = 1 T (1.1) Introduction to Waves and Oscillations 11 where ω is the angular frequency, which is 2 π times the frequency, ν , and T the period of the vibrations; one complete cycle of the wave is associated with an angular displacement of 2 π radians. The angular frequency, ω , of a wave is the number of radians per unit of time at a fixed position. 3. Path difference: The path length, l , is the distance through which a wavefront recedes when the phase increases by δ and is expressed as l = v ω δ = λ 2 π δ = λ 0 2 πn δ (1.2) where v is the velocity, λ the wavelength, λ 0 the wavelength in free space (vacuum), n = c v (1.3) the refractive index for refraction from vacuum into that medium, and c the speed of light in free space.
eBook - PDFApplied Structural and Mechanical Vibrations
Theory and Methods, Second Edition
- Paolo L. Gatti(Author)
- 2014(Publication Date)
- CRC Press(Publisher)
In practical cases, it is often the ability to reproduce the data by a controlled experiment that pro-vides a general criterion to distinguish between the two. 1.3 SOME DEFINITIONS AND METHODS As stated in the introduction, the particular behaviour of a particle, a body or a complex system that moves about an equilibrium position is called oscil-latory motion. It is then natural to try a description of such a particle, body or system by an appropriate function of time x ( t ), whose physical meaning depends on the scope of the investigation and, as often happens in practice, on the available measuring instrumentation: it might be displacement, veloc-ity, acceleration, stress or strain in structural dynamics; pressure or density in acoustics; current or voltage in electronics or any other time-varying quantity. A function that repeats itself exactly after certain intervals of time is called periodic . The simplest case of periodic motion is called harmonic (or sinusoidal) and is mathematically represented by a sine or cosine function; for example x t X t ( 29 = -( 29 cos ω θ (1.4) where: X is the maximum , or peak amplitude (in the appropriate units) ω t − θ is the phase angle (in radians) ω is the angular frequency (in rad/s) θ is the initial phase angle (in radians), which, in turn, depends on the choice of the time origin and can be taken equal to zero if there is no rela-tive reference to other sinusoidal functions The time between two identical conditions of motion is the period T . It is measured in seconds and is the inverse of the frequency ν = ω /2 π , which is expressed in hertz (Hz, with dimensions of s −1 ). As is probably well known to the reader, frequency represents the number of cycles per unit time and for the harmonic function (Equation 1.4) we have the relations ω πν π ω = = = 2 1 2 , T ν (1.5) A plot of Equation 1.4, amplitude versus time, is illustrated in Figure 1.1 where the peak amplitude is taken as X = 1 and the initial phase angle is θ = 0.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
The units of the amplitude depend on the type of wave, but are always in the same units as the oscillating variable. A more general representation of the wave equation is more complex, but the role of amplitude remains analogous to this simple case. For waves on a string, or in medium such as water, the amplitude is a displacement. ________________________ WORLD TECHNOLOGIES ________________________ The amplitude of sound waves and audio signals (which relates to the volume) con-ventionally refers to the amplitude of the air pressure in the wave, but sometimes the amplitude of the displacement (movements of the air or the diaphragm of a speaker) is described. The logarithm of the amplitude squared is usually quoted in dB, so a null amplitude corresponds to −∞ dB. Loudness is related to amplitude and intensity and is one of most salient qualities of a sound, although in general sounds can be recognized independently of amplitude. The square of the amplitude is proportional to the intensity of the wave. For electromagnetic radiation, the amplitude of a photon corresponds to the changes in the electric field of the wave. However radio signals may be carried by electromagnetic radiation; the intensity of the radiation (amplitude modulation) or the frequency of the radiation (frequency modulation) is oscillated and then the individual oscillations are varied (modulated) to produce the signal. Waveform and envelope The amplitude may be constant (in which case the wave is a continuous wave) or may vary with time and/or position. The form of the variation of amplitude is called the envelope of the wave. If the waveform is a pure sine wave, the relationships between peak-to-peak, peak, mean, and RMS amplitudes are fixed and known, as they are for any continuous periodic wave. However, this is not true for an arbitrary waveform which may or may not be periodic or continuous. For a sine wave the relationship between RMS and peak-to-peak amplitude is: .
eBook - PDF- Dave Benson(Author)
- 2006(Publication Date)
- Cambridge University Press(Publisher)
In the case of sound, on the other hand, the motions involved in the wave are in the same direction as the propagation. Waves with this property are called longitudinal waves. −→ Direction of motion Longitudinal waves Sound waves have four main attributes which affect the way they are perceived. The first is amplitude, which means the size of the vibration, and is perceived as loudness. The amplitude of a typical everyday sound is very minute in terms of physical displacement, usually only a small fraction of a millimeter. The second attribute is pitch, which should at first be thought of as corresponding to frequency of vibration. The third is timbre, which corresponds to the shape of the frequency spectrum of the sound (see Sections 1.7 and 2.15). The fourth is duration, which means the length of time for which the note sounds. These notions need to be modified for a number of reasons. The first is that most vibrations do not consist of a single frequency, and naming a ‘defining’ frequency can be difficult. The second related issue is that these attributes should really be defined in terms of the perception of the sound, and not in terms of the sound itself. So, for example, the perceived pitch of a sound can represent a frequency not actually present in the waveform. This phenomenon is called the ‘missing fundamental’, and is part of a subject called psychoacoustics. 1.2 The human ear 7 Attributes of sound Physical Perceptual Amplitude Loudness Frequency Pitch Spectrum Timbre Duration Length Further reading Harvey Fletcher, Loudness, pitch and the timbre of musical tones and their relation to the intensity, the frequency and the overtone structure, J. Acoust. Soc. Amer. 6 (2) (1934), 59–69. 1.2 The human ear In order to get much further with understanding sound, we need to study its percep- tion by the human ear. This is the topic of this section. I have borrowed extensively from Gray’s Anatomy for this description.
- Andrei D. Polyanin, Alexei Chernoutsan(Authors)
- 2010(Publication Date)
- CRC Press(Publisher)
Chapter P4 Oscillations and Waves P4.1. Oscillations ◮ General definitions. Oscillations are repetitive variations in the state of a system such that the state parameters vary in time according to a periodic or almost periodic law. If oscillations occur without external action due to system deviation from a stable equilibrium, the oscillations are said to be free or natural . If the oscillations occur under the action of an external periodic force, then they are said to be forced . The oscillations are characterized by their period T and frequency ν = 1 /T (measured in hertzs : 1 Hz = 1 s – 1 ). The term vibrations is often used in a narrower sense to mean mechanical oscillations, but sometimes is used synonymously with oscillations. P4.1.1. Harmonic Oscillations. Composition of Oscillations ◮ Simple harmonic oscillations. An oscillation of a quantity x is said to be a simple harmonic oscillation (or simple harmonic motion ) if x varies in time t by the law x = A cos( ωt + ϕ 0 ), (P4. 1 . 1 . 1 ) where A is the amplitude , ϕ = ωt + ϕ 0 is the phase , ϕ 0 is the initial phase , and ω = 2 π/T is the angular or circular frequency of the oscillation. The first and second time-derivatives of the quantity x , ˙ x = – Aω sin( ωt + ϕ 0 ) = Aω cos ( ωt + ϕ 0 + π/ 2 ) , ¨ x = – Aω 2 cos( ωt + ϕ 0 ) = Aω 2 cos( ωt + ϕ 0 + π ), (P4. 1 . 1 . 2 ) oscillate harmonically with the same frequency but with amplitudes ωA and ω 2 A and with the phase shifts π/ 2 and π , respectively. Example. If the initial values (at t = 0 ) of the quantity x and its derivative, x ( 0 ) = x 0 and ˙ x ( 0 ) = v 0 , are known, then the amplitude and the initial phase of the oscillation can be determined. The equations x 0 = A cos ϕ 0 and v 0 = – ωA sin ϕ 0 allow one to find A = radicalbig x 2 0 + ( v 0 /ω ) 2 and tan ϕ 0 = – v 0 / ( ωx 0 ).
eBook - PDF- Md Nazoor Khan, Simanchala Panigrahi(Authors)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
Calculate the amplitude of the resultant wave at this point. [Ans Amplitude of either wave] Oscillations and Waves 93 1.12 The ratio of amplitude of two waves is 1 : 4. If these two waves superpose on each other, find the ratio of minimum and maximum amplitudes. [Ans 3 : 5] 1.13 Two waves of the same frequency and same amplitude are reaching a point simultaneously. What should be the phase difference of the two waves so that the amplitude of the resultant wave will be r where r is the amplitude of a wave? [Ans 120°] 1.14 The equation of a stationary wave produced in a stretched string is x 6cos 3 π Ψ = sin(6 p t ), where x and t are measured in centimeters and seconds respectively. Calculate the frequency, amplitude and velocity of its constituent waves. [Ans 3 Hz, 3 cm, 18 cm/s] 1.15 Three harmonic waves are represented by Y 1 = 2 sin ( w t – 30), Y 2 = 5 sin ( w t + 60) and Y 3 = 4 sin ( w t + 30). Find the resultant wave equation if they are superposed. [Ans y = 9.36 sin( w t + 34.72)] 1.16 Two sources vibrating according to the equation Y 1 = 4 sin 2 p t , and Y 1 = 3 sin 2 p t send out waves in all directions with speed 2.40 m/s. Find the equation of motion of a particle 5 m from the first source and 3 m from the second source when angular speed of both waves is 2 p rad/s [Ans y = 3.08 sin(2 p t – 25.3)] 1.17 Two coherent beams of intensities I 1 and I 2 interfere. What will be the maximum and minimum intensity? [Ans ( ) ( ) 2 2 1 2 1 2 , I I I I + − ] 1.18 An electron moves in the x -direction with a speed of 4.8 × 10 5 m/s.
eBook - PDF- Charles A. Bennett(Author)
- 2015(Publication Date)
- Wiley(Publisher)
The term λ represents the spatial period: (x + λ, t ) = A sin 2π λ (x + λ ∓ vt ) = A sin 2π λ (x ∓ vt ) + 2π = (x , t ) The parameter λ is also called the wavelength. It has SI units of meters. Let T represent the temporal period; i.e., the time required for one cycle. The SI unit of T is seconds (s), but it is convenient to use s/cycle as a reminder of what T represents. Since Equation 1.7 is periodic in T, we have (x , t + T ) = A sin 2π λ [x ∓ v (t + T )] = A sin 2π λ (x ∓ vt ) ∓ 2π λ v T T represents the temporal period provided that v T λ = 1 (1.8) or v = λ T (1.9) Thus, a periodic classical wave travels one wavelength λ in one temporal period T . It is customary to define the wave frequency as f = 1 T (1.10) The units of f are cycles /s (SI unit: s −1 ), often referred to as Hertz ( Hz ). In terms of frequency, Equation 1.9 becomes f λ = v (1.11) A plot of (x , t ) vs. x is shown in Figure 1.3(a). Figure 1.3(b) shows a plot of (x , t ) vs. t . A plot such as this could be obtained from data provided by a measuring device located at a particular value of x . It is customary to define the propagation constant as follows: k = 2π λ (1.12) This quantity is also sometimes referred to as the wave number. Since k converts meters to radians, the units are rad / m (SI unit: m −1 ). We may rewrite Equation 1.7 as (x , t ) = A sin k (x ∓ vt ) 10 THE PHYSICS OF WAVES M λ T x t (a) (b) Figure 1.3. Plots of a harmonic wavefunction. (a) A plot of (x , t ) vs. position x . (b) A plot of (x , t ) vs. time using data recorded by a single measuring device located at M in Figure (a). Similarly, we can define the angular frequency: ω = k v = 2π λ v = 2π f (1.13) Since ω converts time to radians, the units are rad /s (SI unit: s −1 ). Note that according to the last result, ω k = v (1.14) In terms of k and ω, Equation 1.7 becomes (x , t ) = A sin(kx ∓ ωt ) Collectively, the terms kx ∓ ωt are called the phase of the harmonic traveling wave.
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