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Sound Waves http://www.youtube.com/watch?v=16VDa65e3Qw

SOUND WAVES Sound is a longitudinal wave produced by a vibration that travels away from the source through solids, liquids, or gases, but not through a vacuum. So sound waves are also Mechanical waves- they require a medium to be transmitted

Since a sound wave consists of a repeating pattern of high pressure and low pressure regions moving through a medium, it is sometimes referred to as a pressure wave. The above diagram can be somewhat misleading if you are not careful. The representation of sound by a sine wave is merely an attempt to illustrate the sinusoidal nature of the pressure-time fluctuations. Do not conclude that sound is a transverse wave which has crests and troughs.

v = λ f v is the speed of the wave λ is the wavelength and To find the speed of a wave…. v is the speed of the wave λ is the wavelength and f is the frequency v = λ f

Example 1: Measurements show that the wavelength of a sound wave in a certain material is 18.0 cm. The frequency of the wave is 1900 Hz. What is the speed of the sound wave? λ = 0.18 m f = 1900 Hz v = λ f = 0.18m (1900 Hz) = 342 m/s

V= 330m/s + 0.6 T The speed of sound in a gas is proportional to the temperature T… V= 330m/s + 0.6 T Where 330 m/s is the speed of sound at 0°C, and T is the temperature in °C. At 20°C the speed is 342 m/s. Substance Speed   (m/s) Air 343* Helium 965 Water 1482 Lead 1960 Steel 5960 Granite 6000 … and the speed of sound depends on the material that the sound is traveling through. The speed depends on the density of the elasticity of the medium.

The rule of “five” for lightning Rule :  See lightning, start counting seconds until sound is heard.  Divide by five to obtain distance of lightning Example:  10 sec / 5 = 2 miles Why? Speed of sound = 342 m/s at 20 °C Speed of light    = 300,000,000 m/s

We detect two characteristic of sound: pitch and loudness. Pitch is how high or low the sound seems. (use forks and wave box) It is measured by the frequency. The higher the frequency the higher the pitch. The lower the frequency the lower the pitch. Loudness refers to the Intensity of a sound. Energy in a wave is show by the amplitude It is measured in decibels (db) (a logarithmic scale)

What we hear depends on the frequency and the intensity of the sound. We hear frequencies in the range of 20 Hz to 20,000 Hz. ultrasonic infrasonic This is called the audible (or Sonic) range.

What we hear is also affected by the motion of the source or us Relative Intensity     Source      Intensity in Decibels Normal breathing 10 Whisper 20 Conversation 60 Street traffic 70 Rock concert 115 Threshold of pain 120 Jet engine 140   What we hear is also affected by the motion of the source or us http://www.youtube.com/watch?v=J43lAESftPs

The movie at left shows a stationary sound source The movie at left shows a stationary sound source. Sound waves are produced at a constant frequency and wave-fronts move symmetrically away from the source at a constant speed v. The observers at A and B, here the same pitched sound. A B http://www.youtube.com/watch?v=BbIcC1I6pZg

In the movie below, the same sound source is radiating sound waves at a constant frequency in the same medium. However, now the sound source is moving to the right with a speed 100m/s B A Notice listener A is receiving waves that are further apart and he hears a lower apparent frequency than before. Notice listener B is receiving waves that are closer together and he hears a higher apparent frequency than before.

DOPPLER EFFECT When a source of sound and/or a listener are moving, the apparent pitch of the sound changes. This phenomenon is known as the Doppler effect. http://www.youtube.com/watch?v=Y5KaeCZ_AaY

DOPPLER EFFECT: The pitch heard by the listener is given by the following equation: Units: Hz f' is the frequency of the sound heard by the listener (observer), fS is the frequency of the sound emitted by the source, v is the speed of sound in air, vS is the velocity of the source, and vo is the velocity of the listener (observer). Sign Convention: (+) for approaching velocities and (-) for receding velocities.

Example 2: A fire truck siren emits sound at a frequency of 400 Hz on a day when the speed of sound is 340 m/s. a. What is the pitch of the sound heard when the truck is moving toward a stationary observer at a speed of 20 m/s? v = 340 m/s fS = 400 Hz vS = 20 m/s     = 425 Hz b. What is the pitch heard when the truck is moving away from the observer at this speed?   = 377.78 Hz vS = - 20 m/s

SOURCES OF SOUND Sound comes from a vibrating object. If an object vibrates with frequency and intensity within the audible range, it produces sound we can hear. MUSICAL INSTRUMENTS String Instruments: guitar, violin and piano Wind Instruments: Open Pipe: flute and some organ pipes Closed Pipe: clarinet, oboe and saxophone Percussion Instruments: Drums, bells, cymbals

As a string vibrates, it sets surrounding air molecules into vibrational motion. (called forced vibrations) The frequency at which these air molecules vibrate is equal to the frequency of vibration of the guitar string. Forced vibrations: the vibration of an object caused by another vibrating object

On a guitar or a violin, the length of the The sounds produced by vibrating strings are not very loud. Many stringed instruments make use of a sounding board or box, sometimes called a resonator, to amplify the sounds produced. The strings on a piano are attached to a sounding board while for guitar strings a sound box is used. When the string is plucked and begins to vibrate, the sounding board or box begins to vibrate as well (forced vibrations). Since the board or box has a greater area in contact with the air, it tends to amplify the sounds. On a guitar or a violin, the length of the strings are the same, but their mass per length is different. That changes the velocity and so the frequency changes. (demo music box)

A guitar or piano string is fixed at both ends and when the string is plucked, standing waves can be produced in the string. Standing waves are produced by interference Resulting in nodes an antinodes 2-antinode http://www.youtube.com/watch?v=uENITui5_jU

Standing Waves The nodes and antinodes remain in a fixed position for a given frequency. There can be more than one frequency for standing waves in a single string. Frequencies at which standing waves can be produced are called the natural (or resonant) frequencies.

Standing Waves Since the ends are fixed, they will be the nodes. The wavelengths of the standing waves have a simple relation to the length of the string. The lowest frequency called the fundamental frequency has only one antinode. That corresponds to half a wavelength:

The other natural frequencies are called overtones The other natural frequencies are called overtones. They are also called harmonics and they are integer multiples of the fundamental. The fundamental is called the first harmonic. The next frequency has two antinodes and is called the second harmonic.

v – velocity is medium in meters/sec The equation for strings is f – frequency in hertz n – number of antinodes L – length of string in meters v – velocity is medium in meters/sec - n can be any integer value greater than one.

Example 3: What is the fundamental frequency of a viola string that is 35.0 cm long when the speed of waves on this string is 346 m/s? L = 0.35 m v = 346 m/s   = 494.2 Hz What is frequency of the third harmonic produced by this string?   = 1482.6 Hz

WIND INSTRUMENTS Wind instruments produce sound from the vibrations of standing waves in columns of air inside a pipe or a tube. In a string, the ends are nodes. In air columns the ends can be either nodes or antinodes. (demo pipes, straw and bottles) Open at both ends pipe Closed at one end pipe

So for an Open tube

For a half-closed tube 4 Why a 4?

HARMONICS a) For open pipe The overtones will be all multiples of the fundamental n = 1, 2, 3, 4 , 5 … b) For closed pipe The harmonics will be the odd multiples of the fundamental n = 1, 3, 5, 7, …

1.32 m long, what is the speed of the waves in the pipe? Example 4: A pipe that is open at both ends has a fundamental frequency of 125 Hz. If the pipe is 1.32 m long, what is the speed of the waves in the pipe? f' = 125 Hz L = 1.32 m  

INTERFERENCE OF SOUND WAVES: BEATS If two sources are close in frequency, the sound from them interferes and what we hear is an alternating sound level. The level rise and falls. If the alternating sound is regular, it is called beats. (Demo tuning forks)

The beat frequency equals the difference in frequencies between the sources. f beats = │f2 – f 1│ This is a way to tune musical instruments. Compare a tuning fork to a note and tune until the beats disappear. CI Constructive Interference DI Destructive

Noise canceling head phones for flights Uses complete destructive interference

v = λ f 4 f beats = │f2 – f 1│ V sound = 340 m/s V light = 3.0 x 108 m/s