Characteristics of Waves

What are waves? Waves are rhythmic disturbances that carry energy through matter or space.

Mechanical Waves Mechanical Waves are those in which their energy is carried through a medium (substance that carries the wave).

Non mechanical Waves Other waves such as light and radio waves, do not need a medium and can travel through the vacuum of space. These are called electromagnetic waves.

Transverse waves Waves in which the disturbance moves particles of the medium up and down are called transverse waves.

Compression wave If the particles of the medium move back and forth, a compression (longitudinal) wave is created Example – sound waves

Parts of the Transverse Wave When you snap a rope up and down, you may notice that high points and low points form. The highest point in the wave is the crest. The lowest point in the wave is the trough.

Amplitude is the distance from the crest or trough to the rest position (equilibrium position). It corresponds to the amount of energy carried by the wave.

wavelength The wavelength is the distance between a point on one wave and an identical point on the next wave, such as from crest to crest or from trough to trough.

Wave Frequency & Period The frequency of a wave is the number of wave crests that pass one place each second. The period of a wave is the time it takes one complete wave to pass a fixed point.

Wave pulse A wave pulse – a single disturbance, moving through the medium from one location to another. The particles are temporarily displaced, but not permanently relocated. Example: Cork on a water wave.

The particles of the medium, such as ocean water, are temporarily displaced, but are not permanently relocated, otherwise water would be moved from the ocean to the shore. There can still be ocean currents that move objects across the ocean.

Wave Fronts Many waves may travel together in a straight line direction, such as successive wave crests that move toward the shore. They may be thought of as wave fronts.

Wave equation

The Medium Determines Velocity if the Wave If the wavelength (λ) increases, the frequency (f) decreases. If the wavelength (λ) decreases, the frequency (f) increases. Therefore in both cases, the velocity of the wave remains constant.

The characteristics of the medium, therefore, determines the velocity of the wave through that medium

Imagine if the velocity of the wave depended upon the changes in frequency or wavelength, instead of the medium. If you went to a concert, even though the music was played in a synchronized fashion, you would hear different pitched instruments at different times. That would not be very pleasant for most of us.

Wave- Sample Problem #1 A wave is generated in a wave pool at a water amusement park. The wavelength is 3.2 m, and the frequency of the wave is 0.60 Hz. What is the velocity of the wave? = 3.2m f = 0.60 Hz v = ? v =  f = (3.2)(0.60Hz) = 1.93 m/s

Wave- Sample Problem #2 If the frequency of the water wave in problem #1 on the previous slide was 0.3 Hz, but the velocity remained the same, what is the wavelength? f = 0.3 Hz v = 1.92 m/s  = ?  = v = 1.92 m/s f 0.3 Hz = 6.4 m (half the frequency = twice the 

Wave- Sample Problem #3 Earthquakes can produce three types of waves. One of these waves is a transverse wave called an S wave. A typical S wave travels at 5000 m/s at 5000 m/s. Its wavelength is 417 m. What is the frequency? = 417 m v = 5000 m/s f = ? f = v = 5000 m/s 417 m = 11.9 Hz

Reflection of Waves Reflection – a wave is turned back when it encounters a barrier in the medium If the barrier is solid, the wave is reflected back almost completely, except it is inverted.

If a wave is at some angle then the law of reflection is observed. The Law of Reflection: The angle of incidence is equal to the angle of reflection. Reflection of Waves

The angle of incidence and reflection are measured in relation to the normal. The normal is an imaginary line perpendicular to the reflective surface. Reflection of Waves

Diffuse and Specular Reflection If a wave is incident on a rough surface, the reflected wave travels in many directions. This is diffuse reflection. (A page that reflects light in a diffuse manner, cuts down on glare, making it easier to read.)

Specular reflection refers to reflection off a surface in which the irregularities are smaller than the wavelength ---such as light reflected off a mirror. Diffuse and Specular Reflection

The ball on the left produces glare when reflecting the light because the reflection is specular, rather than diffuse. Diffuse and Specular Reflection

It is better to have diffuse reflection in a concert hall so that a small amount of sound is reflected from many parts of the wall, rather than a large portion reflected off one part of the wall. Diffuse and Specular Reflection – Used in Concert Halls

Constructive and Destructive Wave Interference Interference is the effect produced when two waves pass through each other in the same medium.

Constructive Interference – individual displacements add to form the resultant wave (amplitudes added). This happens then the wave pulses are on the same side of the equilibrium position. After the waves pulses separate, they go back to their original pulse sizes. Constructive and Destructive Wave Interference

Notice the change in amplitude as the wave pulses combine in this example of constructive interference. This adding of amplitudes is known as superposition. Constructive and Destructive Wave Interference

Destructive Interference – individual displacements are subtracted to form a smaller resultant wave pulse (amplitude is smaller) This happens when the pulses are on opposite sides of the equilibrium position. After the waves pulses separate, they go back to their original pulse sizes. Constructive and Destructive Wave Interference

If the two wave pulses are equal and opposite, they cancel each other out---resulting in complete destructive interference. Constructive and Destructive Wave Interference

Notice when there is complete destructive interference in the waves below. Constructive and Destructive Wave Interference Animation from: Daniel A. Russell, Graduate Program in Acoustics, The Pennsylvania State University

Standing Wave Standing wave – a wave pattern that results when two waves of the same frequency, wavelength and amplitude travel in opposite directions and interfere. Standing wave forms

The points where complete destructive interference happens on a standing wave are called nodes. There is no motion of the string at the nodes. Standing Wave

Midway between two adjacent nodes, the string vibrates with the largest amplitude. This is an antinode, the place of largest displacement. Standing Wave

Refraction and Diffraction A change in wave direction at the boundary between two media is known as refraction. This is caused by the change in velocity of the wave as it passes from one medium to another.

Refraction of light – the light waves bend as they pass through a prism Refraction and Diffraction

Refraction of light as it passes from air to water Refraction and Diffraction

Diffraction – The spreading of waves around obstacles and into the region behind it. Diffraction can occur through an opening, such as slits, or pinhole, etc.) Refraction and Diffraction