Regents Physics - Wave Characteristics
Defining & Describing Waves
A pulse is a single disturbance which carries energy through a medium or through space. Imagine you and your friend holding opposite ends of a slinky. If you quickly move your arm up and down, a single pulse will travel down the slinky toward your friend.
If, instead, you generate several pulses at regular time intervals, you now have a wave carrying energy down the slinky. A wave, therefore is a repeated disturbance which carries energy. The mass of the slinky doesn't move from end of the slinky to the other, but the energy it carries does.
When a pulse or wave reaches a hard boundary, it reflects off the boundary, and is inverted. If a pulse or wave reaches a soft, or flexible, boundary, it still reflects off the boundary, but does not invert.
Waves at Boundaries
Waves can be classified in several different waves. One type of wave, known as a mechanical wave, requires a medium (or material) through which to travel. Examples of mechanical waves include water waves, sound waves, slinky waves, and even seismic waves. Electromagnetic waves, on the other hand, do not require a medium in order to travel. Electromagnetic waves (or EM waves) are considered part of the Electromagnetic Spectrum. Examples of EM waves include light, radio waves, microwaves, and even X-rays.
Further, waves can be classified based upon their direction of vibration. Waves in which the "particles" of the wave vibrate in the same direction as the wave direction are known as longitudinal, or compressional, waves. Examples of longitudinal waves include sound waves and seismic P waves. Waves in which the particles of the wave vibrate perpendicular to the wave's direction of motion are known as transverse waves. Examples of transverse waves include seismic S waves, electromagnetic waves, and even stadium waves (the "human" waves you see at a baseball or football game!).
Transverse vs. Longitudinal
It is important to note that in a transverse wave, the motion of the medium is perpendicular to the direction of the wave's velocity. This is illustrated clearly in the animation below.
Courtesy C.K. Ng
Wave Anatomy
Waves have a number of characterisics which define their behavior. Looking at a transverse wave, we can identify specific locations on the wave. The highest points on the wave are known as crests. The lowest points on the wave are known as troughs. The amplitude of the wave, corresponding to the energy of the wave, is the distance from the baseline to a crest or the baseline to a trough.
The length of the wave, or wavelength, noted with the Greek letter lambda (
), is the distance between corresponding points on consecutive waves (i.e. crest to crest or trough to trough). Points on the same wave with the same displacement from equilibrium moving in the same direction (such as a crest to a crest or a trough to a trough) are said to be in phase (phase difference is 0° or 360°). Points with opposite displacements from equilibrium (such as a crest to a trough) are said to be 180° out of phase.
Question: The diagram represents a periodic wave. Which point on the wave is in phase with point P?
Answer: Point C is in phase with point P, since point C represents a point with the same displacement from equilibrium moving in the same direction. Points that are in phase are located one or more whole wavelengths apart on a wave.
Question: Two waves having the same frequency and amplitude are traveling in the same medium. Maximum constructive interference occurs at points where the phase difference between the two superposed waves is:
Answer: 0°.
In similar fashion, longitudinal, or compressional, waves also have amplitude and wavelength. In the case of longitudinal waves, however, instead of crests and troughs, the longitudinal waves have areas of high density (compressions) and areas of low density (rarefactions), as shown in the representation of the particles of a sound wave. The wavelength, then, of a compressional wave is the distance between compressions, or the distance between rarefactions. Once again, the amplitude corresponds to the energy of the wave.
Question: A longitudinal wave moves to the right through a uniform medium, as shown below. Points A, B, C, D, and E represent the positions of particles of the medium. What is the direction of the motion of the particles at position C as the wave moves to the right?
Answer: The particles move to the left and right at position C, as the particles in a longitudinal wave vibrate parallel to the wave velocity:
Question: Between which two points on the wave could you measure a complete wavelength?
Answer: You could measure a complete wavelength between points A and C, since A and C represent the same point on successive waves.
The Wave Equation
The frequency (f) of a wave describes the number of waves that pass a given point in a time period of one second. The higher the frequency, the more waves that pass. Frequency is measured in number of waves per second (1/s), also known as a Hertz (Hz). If 60 waves pass a given point in a second, the frequency of the wave would be 60 Hz.
Closely related to frequency, the period (T) of a wave describes how long it takes for a single wave to pass a given point, and can be found as the reciprocal of the frequency. Period is a measurement of time, and therefore is measured in seconds. Both frequency and period were introduced earlier in our discussion of circular motion.
Question: What is the period of a 60-hertz electromagnetic wave traveling at 3.0×108 meters per second?
Answer:
Because waves move through space, they must have a velocity. The velocity of a wave is a function of the type of wave, and the medium it travels through. Electromagnetic waves moving through a vacuum, for instance, travel at roughly 3*108 m/s. This value is so famous and common in physics it is given its own symbol, c. When an electromagnetic wave enters a different medium, such as glass, it slows down. If the same wave were to then re-emerge from glass back into a vacuum, it would again travel at c, or 3*108 m/s.
The speed of a wave can be easily related to its frequency and wavelength. Speed of a wave is determined by the wave type and the medium its traveling through. For a given wave speed, as frequency increases, wavelength must decrease, and vice versa. This can be shown mathematically using the wave equation: 
.
Question: In a vacuum, all electromagnetic waves have the same:
- speed
- phase
- frequency
- wavelength
Answer: (1) speed.
Question: The diagram below represents a periodic wave traveling through a uniform medium. If the frequency of the wave is 2.0 hertz, find the speed of the wave.
Answer: The diagram shows a length of 6m for 1.5 wavelengths, therefore the wavelength (
Sound Waves
Sound is a mechanical wave which we observe by detecting vibrations in the inner ear. Typically, we think of sound as traveling through air, therefore the particles vibrating are air molecules. Sound can travel through other media as well, including water, wood, and even steel.
The particles of a sound wave vibrate in a direction parallel with the direction of the sound wave's velocity, therefore sound is a longitudinal wave. The speed of sound in air at standard temperature and pressure (STP) is 331 m/s, a value which is supplied on the front of the Regents Physics Reference Table.
Question: At an outdoor physics demonstration, a delay of 0.50 second was observed between the time sound waves left a loudspeaker and the time these sound waves reached a student through the air. If the air is at STP, how far was the student from the speaker?
Answer:
When we observe sound waves through hearing, we pick up the amplitude, or energy, of the wave as loudness. The frequency of the wave is perceived as pitch, with higher frequencies observed as a higher pitch. Typically, humans can hear a frequency range of 20Hz to 20,000 Hz, although young observers can often detect frequencies above 20,000 Hz, an ability which declines with age.
Certain devices create strong sound waves at a single specific frequency. If another object, having the same "natural frequency," is impacted by these sound waves, it may begin to vibrate at this frequency, producing more sound waves. The phenomenon where one object emitting a sound wave with a specific frequency causes another object with the same natural frequency to vibrate is known as resonance. A dramatic demonstration of resonance involves a singer breaking a glass by singing a high pitch note. The singer creates a sound wave with a frequency equal to the natural frequency of the glass, causing the glass to vibrate at its natural, or resonant, frequency so energetically that it shatters.
Question: Sound waves strike a glass and cause it to shatter. This illustrates what phenomenon?
Answer: Resonance.
