Daily Challenge, 10/26 WHAT IS SOUND? Earlier, we saw how waves on a Slinky can cancel each other, add together to make one big wave, pass through each other, or reflect off a boundary. CAN SOUND WAVES DO ALL THAT?

SONIC SPECTRUM the frequency range over which mechanical longitudinal waves occur the lower limit is undefined (earthquake P wave frequencies ~ Hz, wavelengths that are kilometers long) the upper limit is well defined must be greater than inter-particle spacing for propagation to occur

So what are the upper limits? at ordinary temperature & pressure, upper range of sonic frequency ~ 10 9 Hz in gaseous medium upper range of sonic frequency is higher in solids and liquids because particles are closer together

SOUND a.k.a. audio spectrum the portion of sonic spectrum to which the human ear is sensitive (20 Hz – 20,000 Hz) ultrasonic waves – longitudinal waves at frequencies > sound infrasonic waves – longitudinal waves at frequencies < sound

How are sound waves produced? through a VIBRATION which produces compressions and rarefactions in a medium capable of propagating these waves Air can propagate sound waves, more dense air is better transmitter than less dense air. Liquids are excellent sound transmitters of sound waves. SOME solids are good transmitters of sound waves.

Practice Problem The speed of sound in air is m/s at 0°C and increases with temperature at (0.6 m/s ) / °C Light travels at about 300,000,000 m/s. If lightning strikes one mile away from you, what will be the lag time between seeing the lightning and hearing the thunder?

Daily Challenge, 10/28 The speed of sound in air is m/s at 0°C & increases with temperature at (0.6 m/s )/°C You see a helicopter pass directly overhead. Two seconds later you hear the sound of the engines. If the air temperature is 23°C, how high was the helicopter flying?

FREQUENCY PITCH is the characteristic of sound that depends on the fundamental frequency received by the human ear. NOISE is unpleasant sound, random mix of frequencies MUSIC is pleasant sound octaves have a frequency ratio of 2:1 major chords have frequency ratios of 4:5:6:8

BEATS BEATS are amplitude pulsations through time that result from the interference of two close frequencies. Number of Beats per second = frequency difference in Hz

Sound Intensity Intensity = power / area (Power is measured in Watts, area in m 2 ) Intensity is the time rate at which sound energy flows through a unit area normal to the direction of wave propagation. depends on wave amplitude measured with an acoustical instrument We detect intensity as the LOUDNESS of a sound, but the perception of loudness may vary from ear to ear.

Relative Sound Intensity,   is the intensity compared to the threshold of hearing  on a logarithmic scale due to the great range of human hearing d  = 10 * log (I/I o ) d  is the relative intensity in decibels I is the intensity of the sound I o is the intensity of the threshold of hearing ( assumed to be W/m 2 )

Type of Sound Relative Intensity (d  ) hearing threshold0 whisper10-20 conversation60-70 rock concert110 pain threshold jet engine150

The relative intensity of the sound of a jet engine is 165 dB at a distance of 4.65 meters from the engine. How much sound energy does the engine produce in one minute? Practice Problem

Daily Challenge, 10/29 How is it that we can recognize different people’s voices, even when they sing the same note?

FUNDAMENTAL TONES If a string vibrates as a whole (as a single unit) it produces its lowest frequency, which is called the FUNDAMENTAL tone. A string itself disturbs very little air, so a SOUNDING BOARD is used to make it louder (increasing intensity).

HARMONICS Strings (and other things) may vibrate in segments in addition to vibrating as an entire unit HARMONICS are frequencies that are whole number multiples of the fundamental. The fundamental is called the first harmonic, twice the frequency is the second harmonic, etc. Sound quality or TIMBRE depends on the number of harmonics produced and their relative intensities.

FORCED VIBRATIONS FORCED VIBRATIONS occur when an object in contact with a vibrating object begins to vibrate. SYMPATHETIC VIBRATIONS a.k.a. RESONANCE

RESONANCE occurs when a sound wave causes an object to vibrate at its natural frequency For a closed tube…f = v / (4L + 0.4d) only ODD harmonics are resonant frequencies For an open tube… f = v / (2L + 0.8d) ALL harmonics are resonant frequencies f = frequency of fundamental v = velocity of sound in air L = length of tube d = inside diameter of tube

The Doppler Effect If a sound source and/or listener are moving with respect to each other, the pitch of the sound the listener hears is changed. Listener hears higher pitch as they move together, lower pitch as they move apart. Will it matter whether the sound source is moving toward the listener or the listener is moving toward the sound? YES!

The Doppler Effect getting closer togethergetting further apart Moving Source f LF = f s * v / (v – v s )f LB = f s * v / (v + v s ) Moving Listener f LF = f s * (v + v LC ) / vf LB = f s * (v – v LO ) / v f LF = frequency heard by listener in front of source f LB = frequency heard by listener behind source f s = frequency of sound created by source v = velocity of sound in given medium v s = velocity of the source v LC = closing velocity of the listener v LO = opening velocity of the listener

Applications of the Doppler Effect weather monitoring (Doppler radar) speed measurements (radar & laser guns) Red Shift  Big Bang Theory

Practice Problem The frequency of a particular fire alarm is 3500 Hz. If the alarm is on a fire station and you are driving toward it at 25 m/s, what pitch do you hear? If the alarm is on a fire truck, and the truck is driving toward your stationary position at 25 m/s, what pitch do you hear?

Daily Challenge, 10/30 A physics student blows across the top of a graduated cylinder that is 23.0 cm tall and 4.00 cm in diameter. If the temperature in the room is 21.5°C, what is the frequency of the sound produced?

LAWS OF STRINGS Law of lengths: f/f = l/l the frequency of a string is inversely proportional to its length if all other factors are constant (if your shorten the string, you raise the pitch) Law of diameters: f/f = d/d the frequency of a string is inversely proportional to its diameter if all other factors are constant (smaller diameter strings have higher frequencies, and therefore higher pitches, than larger diameter strings)

LAWS OF STRINGS (continued) Law of tensions: f/f =  F/  F the frequency of a string is directly proportional to the square root of the tension on the string if all other factors are constant (when you tighten a string, you raise the pitch) Law of densities: f/f =  D/  D the frequency of a string is inversely proportional to the square root of its density if all other factors are constant (the more dense a string, the lower the frequency)

Practice Problem The frequencies of two notes in a chord played on a guitar have a ratio of 3:2. If the tension on the first string is 285N, what is the tension on the second string assuming all other factors are equal?

Daily Challenge, 11/2 If I have a guitar string in which I double the tension and cut the vibrating length in half, what will happen to the frequency produced by the string? (Give a quantitative answer.)

Daily Challenge, 11/3 Write down three possible scientific questions you could investigate in a lab studying some aspect of sound.