Traveling Waves Waves and Sound

Traveling Wave A disturbance that travels at a specific speed. Mechanical Wave These are traveling waves that involve the vibrations of a physical substance in a medium. Electromagnetic waves Oscillating electric and magnetic fields that travel can travel without a medium.

Wave Propagation The ways that a wave travels Source A wave must be initiated by a source. Disturbance The oscillations/vibrations of the particles that constitute the medium that a wave moves through. Medium The substance a wave travels in. Speed The speed of the disturbance in the direction the wave is moving.

Transverse Waves Classic sinusoidal waves. Equilibrium: Natural rest point of the oscillators comprising the wave Amplitude, A : Maximum displacement, from equilibrium. Wave length, λ : The length on one wave, measured from a point on one wave to the same point on the next wave. In a transverse wave the oscillating particles in the medium vibrate perpendicular to the direction of wave velocity. Light is transverse wave. λ A Equilibrium λ

Longitudinal Waves λ In a longitudinal wave the oscillating particles in the medium vibrate parallel to the direction of wave velocity. Sound travels as a longitudinal wave, and the dots in the above diagram represent molecules of air vibrating back and forth. The vibration creates regions of high density air known as compressions, and as a result longitudinal waves are also known as compression waves. To create a compression the air becomes less dense between compressions, and these regions are known as rarefactions. Longitudinal waves still follow a sinusoidal mathematical function and they can be shown with a traditional sinusoidal form. When they are do not confuse them with transverse waves. Rarefaction Compression

Period Frequency Time of one cycle The number of cycle each second Used in circular motion, oscillations, and waves. Upper case T is the time (in seconds) of one complete cycle. Lower case t is still used for the time of anything other than one cycle (half a cycle, 10 cycles, etc.) Frequency The number of cycle each second Frequency is how frequently each cycle occurs. The units should be cycles per second. However, since cycles don’t have units. They are a count, and since everything is based on one cycle, the count is 1 . There is also another way to say cycles per second: Hertz

One cycle One period One wavelength Four amplitudes Most students will incorrectly answer 2 amplitudes. Examine one cycle. 1 A 2 3 4

Wave Speed The medium determines wave speed. Several physical properties of the medium influence wave speed. These include density, elasticity, temperature, tension, etc. For waves traveling in a string or wire the medium is the string or wire and speed depends on tension. The greater the tension the greater the speed. For sound the speed depends on several factors, but in general it is tied to density. The denser the medium (air, water, metal, etc.) the faster sound travels through it. Sound cannot travel in a vacuum since there is no medium to allow wave propagation. Light is the opposite of sound. It is the only wave that does not require a medium, and it can travel through a vacuum. Light also travels with the greatest speed in a vacuum and slows as it enters materials with greater density.

Wave Speed Common wave speeds will be found in a table within the text, and should be used to complete this assignment. For comparison, and overall trends, here are some values for the speeds of sound and light in commonly encountered mediums. Sound Light Vacuum 0 m/s 3.00 × 108 m/s Air (20oC) 343 m/s 2.9991 × 108 m/s Water 1480 m/s 2.25 × 108 m/s Diamond 12,000 m/s 1.24 × 108 m/s

Wave Speed If wave speed is determined by the medium, and if the medium is constant, then wave speed will be constant. This means the constant speed equation applies to waves moving in a single, constant, medium. There is also a new equation to determine wave speed, and it is probably the most encountered equation in subsequent sections.

Wave Speed (Constant Medium) If medium is constant, then wave speed is constant. For a constant medium wave speed does not depend on frequency or wavelength. This means that frequency and wavelength will vary inversely . Since they are inversely proportional graphing frequency versus the inverse of wavelength will obtain a linear graph, where the slope is velocity. v f v λ f λ f 1 / λ Slope = v

Wave Speed When the medium remains constant there is a relationship between the energy, frequency, and wavelength of a wave. Wavelength Frequency Energy Short wavelength High frequency High energy Long wavelength Low frequency Low energy

Example 1 The oscillators comprising a wave vibrate 60 times every 3.0 minutes. The wavelength is measured as 30 cm. Determine wave speed.

Example 2 A wave traveling at 28 m/s has a wavelength of 16 cm. Determine the period of the mediums vibration.

Example 3 Light traveling in a vacuum has a wavelength of 460 nm. (A) Determine the frequency. Remember the speed of light in a vacuum is represented by the variable c , which alters the wave speed equation. In addition, it is a known constant. (B) Determine the distance light travels in one year (a light year).