Location: Ch 1: Introduction to Waves

INTRODUCTION TO WAVES IN THIS CHAPTER: Vibrations of a Pendulum Wave Description Wave motion Wave Speed Transverse Waves Longitudinal Waves Interference Standing Waves The Doppler Effect Bow Waves Shock Waves

    If the frequency of a wave is known, the period can be calculated with the following equation: period ´ frequency = 1. When energy travels by a wave, there is no transfer of matter. Instead, the disturbance itself moves. The speed of such a disturbance can be easily calculated with the following equation: wave speed = frequency ´ wavelength.

    There are two types of waves. A transverse wave appears to bounce up and down, perpendicular to the wave’s direction, while a longitudinal wave appears to move along the direction of the wave. Since transverse waves bounce up and down perpendicular to the wave’s direction, they do not need any particles to travel through. Therefore, transverse waves can travel through a vacuum. Electromagnetic waves are transverse since they travel through the vacuum of space. Longitudinal waves, however, require particles to compress and rarefy. Thus, longitudinal waves cannot travel through a vacuum. Since a sound wave uses particles to bounce on our ears, they are longitudinal and also cannot travel through space.

    Unlike a tangible object such as a rock, waves can occupy the same space at the same time. When this happens, interference occurs and the wave effects can be increased, decrease or neutralized. If two crests overlap, constructive interference occurs and the resulting effect appears to be twice as large. However, if a crest overlaps with a trough, the high part of the wave will fill in the low part of the other wave and they cancel each other out. Another interesting thing that can be accomplished with interference is a standing wave. A standing wave is caused by a wave that reflects off a rigid object and interferes with itself, causing areas where the wave does not appear to move at all. Such an area is known as a node. An antinode is an area of a standing wave with the greatest amplitude.

    When an object creates a wave, the wave spreads out from the object in all directions. If the object is at rest, the circles of waves have the same frequency. If the object is moving slower than the wave then something different happens. Then the object appears to be chasing some of the crests it makes. Then the waves in front of the bug increase in frequency. At the same time, the waves in back appear to decrease in frequency. If the object moves faster than the wave then it will produce a bow wave. A bow wave is created when an object moves faster than the crests it produces. A shock wave is a bow wave that travels through time and space. Another interesting thing happens if a sound source moves at a different speed than the receiver. This is known as the Doppler effect. The apparent change in frequency only occurs when there is relative motion between the source and the receiver. The Doppler effect can be seen when a fire truck passes a person. When it moves toward you, the increase in frequency causes the fire truck’s siren to seem higher-pitched. As it moves away, the decrease in frequency of the fire truck’s siren makes its sound lower-pitched.

    An oscilloscope is a device that takes vibrations and shows them in time as a graph on a Cartesian plane. It takes input in electrical voltage. If the voltage varies, you get a sine curve on the graph. However, the oscilloscope’s graph is always a transverse wave. An oscilloscope’s graph shows time on the X-axis and volts (the input) as the Y-axis. This input voltage can be from any source, such as a light sensor, a microphone or even a scale. If the input voltage varies, then a sine wave will be produced. A perfect tone from a musical instrument produces a standing wave on the graph.

    In conclusion, a vibration is a wiggle in time and a wave is a vibration through space. A period is how long it takes to do a back and forth vibration. The wavelength is the distance between identical parts of a wave. Waves carry energy but do not transfer matter anywhere. There are two types of waves. In a transverse wave, the medium moves perpendicular to the wave’s direction and does not require particles. Electromagnetic waves are transverse waves. In a longitudinal wave, the medium moves back and forth, parallel to the wave’s direction. Sound waves are longitudinal. Interference occurs when two waves occupy the same space and change the wave effect. Constructive interference is caused by two crests or troughs overlapping, while destructive interference results from a crest overlapping a trough. A standing wave is caused by a wave reflecting and interfering with itself, causing some parts of the wave to appear to be not moving at all. The Doppler effect is an apparent change in frequency due to relative motion between the source and receiver. Finally, when an object moves through a medium faster than the waves it generates, a bow wave or shock wave spreads out behind it.

Location: Ch 1: Introduction to Waves