Category: Waves—I

Consider a string, such as a guitar string, that is stretched between two clamps. Suppose we send a continuous sinusoidal wave of a certain frequency along the string, say, toward the right. When the wave reaches the right end, it reflects and begins to travel back to the left. That left-going wave then overlaps the…

In Section 16-10, we discussed two sinusoidal waves of the same wavelength and amplitude traveling in the same direction along a stretched string. What if they travel in opposite directions? We can again find the resultant wave by applying the superposition principle. Figure 16-19 suggests the situation graphically. It shows the two combining waves, one traveling to the left…

We can represent a string wave (or any other type of wave) vectorially with a phasor. In essence, a phasor is a vector that has a magnitude equal to the amplitude of the wave and that rotates around an origin; the angular speed of the phasor is equal to the angular frequency ω of the wave. For example, the…

Suppose we send two sinusoidal waves of the same wavelength and amplitude in the same direction along a stretched string. The superposition principle applies. What resultant wave does it predict for the string? The resultant wave depends on the extent to which the waves are in phase (in step) with respect to each other—that is, how much…

It often happens that two or more waves pass simultaneously through the same region. When we listen to a concert, for example, sound waves from many instruments fall simultaneously on our eardrums. The electrons in the antennas of our radio and television receivers are set in motion by the net effect of many electromagnetic waves…

As a wave passes through any element on a stretched string, the element moves perpendicularly to the wave’s direction of travel. By applying Newton’s second law to the element’s motion, we can derive a general differential equation, called the wave equation, that governs the travel of waves of any type. Figure 16-13a shows a snapshot of a…

When we set up a wave on a stretched string, we provide energy for the motion of the string. As the wave moves away from us, it transports that energy as both kinetic energy and elastic potential energy. Let us consider each form in turn. Kinetic Energy A string element of mass dm, oscillating transversely in…

The speed of a wave is related to the wave’s wavelength and frequency by Eq. 16-13, but it is set by the properties of the medium. If a wave is to travel through a medium such as water, air, steel, or a stretched string, it must cause the particles of that medium to oscillate as it passes. For…

Figure 16-8 shows two snapshots of the wave of Eq. 16-2, taken a small time interval Δt apart. The wave is traveling in the positive direction of x (to the right in Fig. 16-8), the entire wave pattern moving a distance Δx in that direction during the interval Δt. The ratio Δx/Δt (or, in the differential limit, dx/dt) is the wave speed v. How can we…

To completely describe a wave on a string (and the motion of any element along its length), we need a function that gives the shape of the wave. This means that we need a relation in the form y = h(x, t), in which y is the transverse displacement of any string element as a function h of the time t and the position x of the…