Author: yasir
-
The Speed of a Traveling Wave
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…
-
Wavelength and Frequency
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…
-
Transverse and Longitudinal Waves
A wave sent along a stretched, taut string is the simplest mechanical wave. If you give one end of a stretched string a single up-and-down jerk, a wave in the form of a single pulse travels along the string, as in Fig. 16-1a. This pulse and its motion can occur because the string is under tension. When you…
-
Types of Waves
Waves are of three main types: 1. Mechanical waves. These waves are most familiar because we encounter them almost constantly; common examples include water waves, sound waves, and seismic waves. All these waves have two central features: They are governed by Newton’s laws, and they can exist only within a material medium, such as water, air, and…
-
Waves—I
How could the submarine’s depth be determined from measurements made very far away? The answer is in this lesson. In August 2000, as Russia’s Northern Fleet conducted exercises in the Barents Sea north of Russia, the nuclear submarine Kursk mysteriously sank. As word of the loss spread, seismologists from around the Northern Hemisphere realized that, on the…
-
Forced Oscillations and Resonance
A person swinging in a swing without anyone pushing it is an example of free oscillation. However, if someone pushes the swing periodically, the swing has forced, or driven, oscillations. Two angular frequencies are associated with a system undergoing driven oscillations: (1) the natural angular frequency ω of the system, which is the angular frequency at which it would oscillate if it were suddenly disturbed…
-
Damped Simple Harmonic Motion
A pendulum will swing only briefly underwater, because the water exerts on the pendulum a drag force that quickly eliminates the motion. A pendulum swinging in air does better, but still the motion dies out eventually, because the air exerts a drag force on the pendulum (and friction acts at its support point), transferring energy from…
-
Simple Harmonic Motion and Uniform Circular Motion
In 1610, Galileo, using his newly constructed telescope, discovered the four principal moons of Jupiter. Over weeks of observation, each moon seemed to him to be moving back and forth relative to the planet in what today we would call simple harmonic motion; the disk of the planet was the midpoint of the motion. The…
-
Pendulums
We turn now to a class of simple harmonic oscillators in which the springiness is associated with the gravitational force rather than with the elastic properties of a twisted wire or a compressed or stretched spring. The Simple Pendulum If you hang an apple at the end of a long thread fixed at its upper…
-
An Angular Simple Harmonic Oscillator
Figure 15-7 shows an angular version of a simple harmonic oscillator; the element of springiness or elasticity is associated with the twisting of a suspension wire rather than the extension and compression of a spring as we previously had. The device is called a torsion pendulum, with torsion referring to the twisting. Fig. 15-7 A torsion pendulum is an angular version of…