# Waves

A **wave** is a self-sustaining disturbance of a medium that travels from one point to another, carrying energy and momentum. The waves travel but the particles within the medium do not. The particles only oscillate in place. Energy is carried by the wave from the source. The direction of energy transport is called the **direction** (line) of propagation of the wave. Any wave in which the vibration is perpendicular to the direction of **propagation** is called a **transverse** **wave**.

Typical transverse waves are electromagnetic waves - light, radio, etc. Waves in which the vibration is parallel to the direction of propagation is called a **longitudinal** (compression) wave.

**Wave Anatomy**

The **period** (T) of a wave is the time it takes the wave to go through one complete cycle. The period is the number of seconds per cycle. The **frequency** (f) of a wave is the number of cycles per second, or Hertz (Hz).

The top of the waves (as shown by points A and F above) are called **crests**. The bottom points of the wave ( as shown by points D and I above) are called **troughs**. The crests and troughs continue to move with speed v, the wave speed. The **amplitude** of a wave is the maximum disturbance undergone during a vibration cycle.

The wavelength is the distance along the direction of propagation between corresponding points on the wave (distance from A to F, C to H, B to G, or D to I for example above). The stationary points of a wave (B, E, and G above) are called **nodes** (see below). The point of greatest motion (crest) is called an **antinode** (see below). The portion of a wave between adjacent nodes is called a wave **segment**. It is one half a full wave length.

**Wave Behavior**

A **standing wave** is the result of identical waves moving in opposite directions. The system undergoes resonance rather than propagation as previously discussed. They do not transport energy or momentum and may not be considered true waves.

The **Law of Reflection** states that the angle at which a wave approaches (angle of incidence) is equal to the angle at which the wave is reflected (angle of reflection). The line drawn at a right angle (perpendicular) to the barrier is called the **normal**.

**Refraction** is the change of wave direction at the boundary between two media. It is refraction of light that produces rainbows and allows vision to be corrected.

**Diffraction** is the bending of waves around an object in its path. The smaller the wavelength in comparison to the size of the obstacle, the less the diffraction.

**Review Questions:**

1. Jimmy goes hiking and shouts at Greg on a vertical cliff 685 away. His echo is heard 4.00 s later. What is the speed of sound of his voice in air?

*v = 343 m/s*

2. If the wavelength of Jimmy's voice is 0.750 m, what is the frequency?

*f= 457 Hz*

3. What is the period of the sound wave Jimmy produces?

*T = 2.19 ms*

4. Crystal starts to get seasick atop the Sears building in Chicago as it sways back and forth in the wind with a frequency of about 0.10 Hz. What is the period of vibration?

*T = 10 s*

5. DeWayne is body surfing in the ocean. If the ocean wave has a length of 10.0 m and a wave passes every 2.0 s, what is the speed of the wave?

*v = 5.0 m/s*

6. The frequency of yellow light is 5.0 x 10*14 Hz. What is the wavelength of yellow light? The speed of light is 300,000 km/s.

*wavelength = 6.0 x 10*-7 m*

7. FM frequencies range between 88 MHz and 108 MHz (megahertz) and travel at the same speed. What is the range of FM wavelengths?

*Frequency range is 2.8 m to 3.4 m*

8. Eric and David are resting on an offshore raft after a swim. They estimate that 3.0 m separates a trough and an adjacent crest of surface waves on the lake. They count 14 crests that pass by the raft in 20.0 s. How fast are the waves moving?

*wavelength = 6.0 m; f = 0.70 Hz; v = 4.2 m/s*

9. William is visiting relatives in California and gets caught in an earthquake. The velocity of the transverse waves produced by the earthquake is 8.9 km/s and that of the longitudinal waves is 5.1 km/s. He records on his seismograph, which he just happens to have with him, that the arrival of the transverse waves comes 73 s before the arrival of the longitudinal waves. How far away was the earthquake?* *

*t = 98 s; d = vt = 870,000 m*

10. Dan likes to play around in the bath tub. One day he tries to create a standing wave in the tub by sloshing the water back and forth at the right frequency. He makes a standing wave in a 150 cm long tub with a frequency of 0.30 Hz. What is the velocity of the water wave?

*v = 0.90 m/s*