14 Chapter Sound Producing a Sound Wave Sound waves are longitudinal waves traveling through a medium A tuning fork can be used as an example of producing a sound wave Using a Tuning Fork to Produce a Sound Wave Using a Tuning Fork, cont. Using a Tuning Fork, final As the tuning fork continues to vibrteate a succession of waves move Categories of Sound Waves
Audible waves
Lay within the normal range of hearing of the human ear Normally between 20 Hz(can be heard by people, but not all people) to 20,000 Hz (some young people can hear it)
Infrasonic waves Ultrasonic waves
Frequencies are below the audible range Earthquakes are an example
Frequencies are above the audible range Dog whistles are an example Applications of Ultrasound Can be used to produce images of small objects Widely used as a diagnostic and treatment tool in medicine Ultrasonic flow meter to measure blood flow May use piezoelectric devices that transform electrical energy into mechanical energy Reversible: mechanical to electrical Ultrasounds to observe babies in the womb Cavitron Ultrasonic Surgical Aspirator (CUSA) used to surgically remove brain tumors Ultrasonic ranging unit for cameras Speed of Sound in a Liquid In a liquid, the speed depends on the liquid's compressibility and inertia V= /
(Elastic property/ inertial property) B is the Bulk Modulus of the liquid is the density of the liquid Compares with the equation for a transverse wave on a string Speed of Sound in a Solid Rod The speed depends on the rod's compressibility and inertial properties
Y is the Young's Modulus of the material is the density of the material
Speed of Sound, General
The
speed of sound is higher in solids than in gases The molecules in a solid interact more strongly The speed is slower in liquids than in solids Liquids are more compressible Speed of Sound in Air
V=(331m/s)(T/273 K)
331 T is
m/s is the speed of sound at 0 C the absolute temperature What is the speed of sound at 0 degrees Celsius? What is the speed of sound at 25 degrees Celsius? As the temperature goes up so does the speed of sound Whuch of the following actions will increase the speed of sound in air? Quick quiz A.) decreasing the air temperature B.) increasing the frequency of the sound C) increasing the air temperature D.) increasing the amplitude of the sound wave E. ) reducing the pressure of the air
As an air plane flying with constant velocity moves from a cold air mass into a warm air mass, does the Mach number *A.) increase B.) decrease *C) remain the same * is the right answer The titanic moving through the night where the temperature is 0 degrees C, sounds its horn and hears an echo 1.00 sec later. What is the distance to the iceberg? 331/2= 331 is the velocity Intensity of Sound Waves
The
average intensity of a wave is the rate at which the energy flows through a unit area, A, oriented perpendicular to the direction of travel of the wave
I = (1/A) - E/t=
The
rate of energy transfer is the power 2 Units are W/m Various Intensities of Sound Threshold of hearing Faintest sound most humans can hear -12 About 1 x 10 W/m2 Threshold of pain Loudest sound most humans can tolerate 2 About 1 W/m The ear is a very sensitive detector of sound waves 10 It can detect pressure fluctuations as small as about 3 parts in 10 Intensity Level of Sound Waves = 10 log (I/Io) The sensation of loudness is logarithmic in the human hear is the intensity level or the decibel level of the sound Io is the threshold of hearing Various Intensity Levels Threshold of hearing is 0 dB Threshold of pain is 120 dB Jet airplanes are about 150 dB Table 14.2 lists intensity levels of various sounds Multiplying a given intensity by 10 adds 10 dB to the intensity level Spherical Waves Intensity of a Point Source 2 Since the intensity varies as 1/r , this is an inverse square relationship The average power is the same through any spherical surface centered on the source \ 2 I = p av/A = p av/ 4r To compare intensities at two locations, the inverse square relationship can be used I1/I2 = r22/ Representations of Waves Plane Wave Doppler Effect A Doppler effect is experienced whenever there is relative motion between a source of waves and an observer. When the source and the observer are moving toward each other, the observer hears a higher frequency When the source and the observer are moving away from each other, the observer hears a lower frequency Doppler Effect, cont. Although the Doppler Effect is commonly experienced with sound waves, it is a phenomena common to all waves Assumptions: The air is stationary
All speed measurements are made relative to the stationary medium Doppler Effect, Case 1 Fo = fs(v+vo/v)
(Observer Toward An Source) observer is moving toward a stationary source Due to his movement, the observer detects an additional number of wave fronts The frequency heard is increased Doppler Effect, Case 1 (Observer Away from Source) Doppler Effect, Case 1 Equation When moving toward the stationary source, the observed frequency is Fo = fs (v/v-vs) moving away from the stationary source, substitute vo for vo in the above equation
When
Doppler Effect, Case 2 (Source in Motion) Doppler Effect, Source Moving Equation
the vs when the source is moving toward the observer and +vs when the source is moving away from the observer Doppler Effect, General Case Both the source and the observer could be moving
Use
Use
positive values of vo and vs if the motion is toward Frequency appears higher Use negative values of vo and vs if the motion is away Frequency appears lower A police man is standing at the side of the road sends out a radar signal of 4000 kHz. If the radar detector is traveling toward the source at 29.0 m/s what is the frequency it will pick up. Shock Waves Shock Waves, cont Tangent lines are drawn from Sn to the wave front centered on So The angle between one of these tangent lines and the direction of travel is given by sin = v / vs The ratio v/vs is called the Mach Number The conical wave front is the shock wave Shock Waves, final
Shock waves carry energy concentrated on the surface of the cone, with correspondingly great pressure variations A jet produces a shock wave seen as a fog
Interference of Sound Waves Sound waves interfere Constructive interference occurs when the path difference between two waves' motion is zero or some integer multiple of wavelengths path difference = n Destructive interference occurs when the path difference between two waves' motion is an odd half wavelength path difference = (n + ) Standing Waves When a traveling wave reflects back on itself, it creates traveling waves in both directions The wave and its reflection interfere according to the superposition principle With exactly the right frequency, the wave will appear to stand still This is called a standing wave Standing Waves, cont A node occurs where the two traveling waves have the same magnitude of displacement, but the displacements are in opposite directions Net displacement is zero at that point The distance between two nodes is An antinode occurs where the standing wave vibrates at maximum amplitude Standing Waves on a String Standing Waves, cont. The pink arrows indicate the direction of motion of the parts of the string All points on the string oscillate together vertically with the same frequency, but different points have different amplitudes of motion Standing Waves on a String, final Standing Waves on a String Frequencies 1, 2, 3 form a harmonic series 1 is the fundamental and also the first harmonic 2 is the second harmonic Waves in the string that are not in the harmonic series are quickly damped out In effect, when the string is disturbed, it "selects" the standing wave frequencies Forced Vibrations A system with a driving force will force a vibration at its frequency When the frequency of the driving force equals the natural frequency of the system, the system is said to be in resonance An Example of Resonance Other Examples of Resonance Child being pushed on a swing Shattering glasses
Tacoma Narrows Bridge collapse due to oscillations by the wind Upper deck of the Nimitz Freeway collapse due to the Loma Prieta
earthquake Standing Waves in Air Columns If one end of the air column is closed, a node must exist at this end since the movement of the air is restricted If the end is open, the elements of the air have complete freedom of movement and an antinode exists Tube Open at Both Ends Resonance in Air Column Open at Both Ends In a pipe open at both ends, the natural frequency of vibration forms a series whose harmonics are equal to integral multiples of the fundamental frequency Tube Closed at One End Resonance in an Air Column Closed at One End The closed end must be a node The open end is an antinode
There
are no even multiples of the fundamental harmonic
Beats Quality of Sound Tuning Fork Quality of Sound Flute Quality of Sound Clarinet Timbre In music, the characteristic sound of any instrument is referred to as the quality of sound, or the timbre, of the sound The quality depends on the mixture of harmonics in the sound Pitch Pitch is related mainly, although not completely, to the frequency of the sound Pitch is not a physical property of the sound Frequency is the stimulus and pitch is the response It is a psychological reaction that allows humans to place the sound on a scale The Ear Frequency Response Curves