Search results
Period—time it takes to complete one oscillation. For waves, these variables have the same basic meaning. However, it is helpful to word the definitions in a more specific way that applies directly to waves: Amplitude—distance between the resting position and the maximum displacement of the wave.
- 17.1 Understanding Diffraction and Interference
where c = 3.00 × 10 8 c = 3.00 × 10 8 m/s is the speed of...
- 2.3 Position Vs. Time Graphs
As we said before, d 0 = 0 because we call home our O and...
- 9.1 Work, Power, and The Work–Energy Theorem
The subscripts 2 and 1 indicate the final and initial...
- 23.3 The Unification of Forces
As discussed earlier, the short ranges and large masses of...
- 9.2 Mechanical Energy and Conservation of Energy
14.1 Speed of Sound, Frequency, and Wavelength; 14.2 Sound...
- 22.4 Nuclear Fission and Fusion
As shown in Figure 22.26, a neutron strike can cause the...
- 23.1 The Four Fundamental Forces
Note to the students that the voltage gap reverses direction...
- 8.2 Conservation of Momentum
where p′ 1 and p′ 2 are the momenta of cars 1 and 2 after...
- 17.1 Understanding Diffraction and Interference
To find the amplitude, wavelength, period, and frequency of a sinusoidal wave, write down the wave function in the form \(y(x, t)=A \sin (k x-\omega t+\phi)\). The amplitude can be read straight from the equation and is equal to \(A\). The period of the wave can be derived from the angular frequency \( \left(T=\frac{2 \pi}{\omega}\right)\).
To derive an equation for the period and the frequency, we must first define and analyze the equations of motion. Note that the force constant is sometimes referred to as the spring constant. Equations of SHM. Consider a block attached to a spring on a frictionless table (Figure 15.4).
The speed of sound in a solid the depends on the Young’s modulus of the medium and the density, \[v = \sqrt{\frac{Y}{\rho}} \ldotp \label{17.5}\] In an ideal gas (see The Kinetic Theory of Gases), the equation for the speed of sound is \[v = \sqrt{\frac{\gamma RT_{K}}{M}}, \label{17.6}\]
In the previous section, we described periodic waves by their characteristics of wavelength, period, amplitude, and wave speed of the wave. Waves can also be described by the motion of the particles of the medium through which the waves move.
Notice that each select point on the string (marked by colored dots) oscillates up and down in simple harmonic motion, between y = + A and y = −A, with a period T. The wave on the string is sinusoidal and is translating in the positive x -direction as time progresses.
This equation is similar to the periodic wave equations seen in Waves, where \(\Delta\)P is the change in pressure, \(\Delta P_{max}\) is the maximum change in pressure, \(k = \frac{2 \pi}{\lambda}\) is the wave number, \(\omega = \frac{2 \pi}{T} = 2 \pi f\) is the angular frequency, and \(\phi\) is the initial phase.
