Waves and SoundChapter 16

16.1 The Nature of Waves

A Wave:1. Traveling disturbance2. Carries energy from place to place

Two Different Types:3. Transverse4. Longitudinal

Slinky

• If the end is jerked up and down, an upward pulse is sent traveling toward the right.

• If the end is then jerked down, a downward pulse is generated and also moves to the right.

Transverse Wave

• Wave in which the disturbance occurs perpendicular to the direction of travel of the wave.

Ex. Radio waves, light waves, microwaves, guitars and banjo strings

Longitudinal Wave

• The disturbance occurs parallel to the line of travel of the wave.

• Ex. Sound wave

Transverse and Longitudinal

• Some waves have both.• Water waves• Particles at the surface move on nearly

circular paths.

16.2 Periodic Waves

• Transverse and longitudinal waves are types of periodic waves.

• Cycles or patterns that are produced over and over again by the source.

• Cycle: • Amplitude A: maximum excursion of a particle of the

medium from the particle’s undisturbed position. Distance between a crest, or highest point on the wave pattern, distance between a trough, or lowest point on the wave pattern.

• Wavelength: horizontal length of one cycle of the wave, horizontal distance between two successive crests.

• Period T: time required for one complete up/down cycle, just as it is for an object vibrating on a spring. Time required to travel one wavelength.Frequency: cycles per second or Hertz Hz

Example

Ex. One cycle of a wave takes one-tenth of a second to pass an observer, then ten cycles pass the observer per second.

F = 1/(0.1s) = 10 cycles/s = 10 Hz

Train example

• Fig 16.6• Train moves by at a constant speed v. The train consists

of a long line of identical boxcars, each of which has a length and requires a time T to pass, so the speed is

v = /T Same equation applies for a wave and relates the speed of the wave to the wavelength and the period T. Since the frequency of a wave is f = 1/T, the expression for the speed is

Example 1: The Wavelengths of Radio Waves

• AM and FM radio waves are transverse waves consisting of electric and magnetic disturbances traveling at a speed of 3.00 x 10^8 m/s. A station broadcasts an AM radio wave whose frequency is 1230 x 10^3 Hz (1230 kHz on the dial) and an FM radio wave whose frequency is 91.9 x 10^6 Hz (91.9 MHz on the dial). Find the distance between adjacent crests in each wave.

The distance between adjacent crests is the wavelength . Since the speed of each waves is v = 3.00 x 10^8 m/s and the frequencies are known, the relation v = f can be used to determine the wavelengths.

Slinky Experiment

HOMEWORKPg. 5041, 2, 3, 4, 5

Terminology

Crest: the top of a waveTrough: the bottom of a waveAmplitude: how far the material is displaced from

rest (from crest to trough)Wavelength: the length of one full wave (between

two identical points, like two crests)Speed: how fast the wave movesFrequency: how many waves there are in a certain

amount of time.

16.3 The Speed of a Wave on a String

• A wave travels faster on a string whose particles have a small mass, or as, it turns out, on a string that has a small mass per unit length.

• Linear density: mass per unit length. (m/L)• Tension F relates to velocity and m and

Length.

• The motion of transverse waves along a string is important in the operation of musical instruments.

Example 2: Waves Traveling on Guitar Strings

• Transverse waves travel on each string of an electric guitar after the string is plucked. The length of each string between its two fixed ends is 0.628m, and the mass is 0.208g for the highest pitched E string and 3.32g for the lowest pitched E string. Each string is under a tension of 226N. Find the speeds of the waves on the two strings.

16.4 The Mathematical Description of a Wave

• When a wave travels through a medium, it displaces the particles of the medium from their undisturbed positions.

• Suppose we would like to know the displacement y of a particle on a wave from its undisturbed position at any time t as the wave passes.

• Involves a sine or cosine

• Displacement of a particle caused by a wave traveling in the +x direction (to the right).

x/v is the time needed for the wave to travel the distance x.

The simple harmonic motion that occurs at x is delayed by the time interval x/v compared to the motion at the origin.

*When a calculator is used to evaluate the functions

It must be set to its radian mode.

Practice Problem #22

The displacement (in meters) of a wave is given according to y=0.26sin

Where t is in seconds and x is in meters. (a) Is the wave traveling in the +x or –x direction? (b) What is the displacement y when t=38s and x=13m?

16.5 The Nature of Sound

• Sound: longitudinal wave, created by a vibrating object.

• Sound can be created or transmitted only in a medium.

• Sound cannot exist in a vacuum.

Loudspeaker

• When the diaphragm of a loudspeaker moves outward, it compresses the air directly in front of it.

• Compression causes the air pressure to rise slightly.

• Condensation: region of increased pressure.• It travels away from the speaker at the speed

of sound.

• After producing a condensation, the diaphragm reverses its motion and moves inward. The inward motion produces a region known as a rarefaction, where the air pressure is slightly less than normal.

• The rarefaction also travels away from the speaker at the speed of sound.

• Wavelength is the distance between the centers of two successive condensations.

• Also the distance between the centers of two successive rarefactions.

The Frequency of a Sound Wave

• Each cycle of a sound wave includes one condensation and one rarefaction.

• Frequency: number of cycles per second that passes by a given location.

• Pure tone: sound with a single frequency.• Healthy young person hears all sound frequencies from

approximately 20 – 20,000Hz.• The ability to hear the high frequencies decreases with age.• Middle aged adult hears frequencies only up to 12-14,000Hz.• http://www.youtube.com/watch?v=4G60hM1W_mk&featur

e=fvwrel

• http://www.youtube.com/watch?v=00y198cE-IU&feature=related

• Infrasonic: sound waves with frequencies below 20Hz.

• Ultrasonic: frequencies above 20kHz.• Bats: up to 100kHz• Rhinoceroses: low as 5Hz to call one another

• A listener’s perception of frequency is subjective.

• The brain interprets the frequency detected by the ear primarily in terms of the subjective quality called pitch.

• A pure tone with a large (high) frequency is interpreted as a high-pitched sound.

• Pure tone with a small (low) frequency is interpreted as a low-pitched sound.

The Pressure Amplitude of a Sound Wave

• When a pure-tone wave travels through a tube filled with air.

• Air pressure varies sinusoidally along the length of the tube.

• Pressure amplitude: magnitude of the maximum change in pressure, measured relative to the undisturbed or atmospheric pressure.

• The pressure fluctuations in a sound wave a normally very small.

Loudness

• Attribute of sound that depends primarily on the amplitude of the wave, the larger the amplitude, the louder the sound.

• Pressure amplitude is an objective property of a sound wave, since it can be measured.

• Loudness, is subjective. (each person determines what is loud)

Speed of Sound