Chapter 25Vibrations and Waves

Vibration – a mechanical occillation around an equilibrium point

Wave - a progressive disturbance propagated from point to point in a medium or space without progress or advance by the points themselves, as in the transmission of sound or light.

• For a pendulum, time it takes the pendulum arm to swing back and forth once is called the period. The period of a pendulum depends on the length of the pendulum arm and the acceleration of gravity.

Simple Harmonic Motion

• The back-and-forth vibratory motion (often called oscillatory motion) of a swinging pendulum is called simple harmonic motion.

Wave Description:Crests – “high” points in a wave

Troughs – “low’ points in a wave

Wavelength – the distance between successive identical parts of a wave (ex. Distance from one wave crest to another wave crest).

Amplitude – the distance from the mid-point to the crest or trough

Frequency – how often a vibration occurs

Hertz – unit of frequency

Period = 1 frequency

Frequency = 1 period

1. What is the frequency in vibrations per second of a 100 Hz wave?

100 vibrations per second

2. The Sears Building in Chicago sways back and forth at a frequency of about .1 Hz. What is its period of vibration?

10 seconds

Wave Speed• Wave speed can be calculated by using the following equation:

wave speed = wavelength x frequency

or: ѵ = λ f

Example: A train passes by at a rate of 2 cars per second. Each train car is 10 meters long. How fast is the train moving?

V = (10 meters)(2 cars/sec)

V = 20 m/s

Wave Speed• The speed of a wave depends on the medium through which the wave moves.

• Sound waves travel about 330 to 350 m/s in air depending on temperature

• How fast does sound travel at room temperature? (25 C)

331 + (.6)(25)

346 m/s

v = 331 m/s + (0.6 m/s/C)•T

Wave TypesTransverse Wave – whenever the motion of the medium is at right angles to the direction which a wave travels, the wave is a transverse wave.

Longitudinal Wave – when the particles in a medium move back and forth in the same direction in which the wave travels.

Interference

• If two rocks are dropped in a pond at the same time, they both produce waves in the water. These waves can overlap to produce an interference pattern.

• If the crest of one wave overlaps the crest of another wave, the effects add together. This is constructive interference.

• If the high part of one wave simply fills the low part of another wave, the effects cancel each other out. This is called destructive interference.

http://en.wikipedia.org/wiki/File:Two_sources_interference.gif