Sound

1. Sound Chapter 13

2. Sound Waves • Sound waves are areas of alternating high and low molecular densities. • Longitudinal • Caused by vibrations • Compression-areas of high molecular density • Rarefactions-areas of low molecular density

3. Speed of Sound • The speed of sound depends on the medium in which it propagates. • Solids Liquids Gases • Hot Cold • (Fast to Slow)

4. Human Hearing • Audible Sounds • Humans can hear frequencies (known as pitch) between 20 Hz and 20,000 Hz • Frequencies higher than we can hear… • Ultrasonic • Frequencies lower than we can hear… • infrasonic

5. Sound Characteristics • Pitch-results from differences in frequency • The higher the frequency, the higher the pitch • Don’t directly observe wavelength • Infrasonic and Ultrasonic • Loudness-results from amplitude • Logarithmic relationship between intensity and perceived loudness. • Increasing intensity by 10 times only results in a doubling of perceived loudness.

6. Intensity • Rate at which energy flows • Inverse square relationship • Units of W/m2 • We will assume the sound spreads in all directions equally so the area we are dealing with is the surface area of a sphere (4πr2).

7. Intensity and Human Hearing • Intensity ranges: • Threshold of Hearing to Threshold of Pain • 1.0 x 10-12W/m2 to 1 W/m2 • This is a large range: • Logarithmic scale compresses this range • Use Decibel levels

8. The Decibel Scale • Hearing damage starts at 85dB • For each 10dB step, the intensity increases by 10 times and the perceived loudness increases by 2 times.

9. Examples • Calculate the intensity of the sound waves from an electric guitar’s amplifier at a distance of 5.0 m when its power output is equal to each of the following values: • 0.25 W • 0.50 W • 2.0 W • If the intensity of a person’s voice is 4.6 x 10-7W/m2 at a distance of 2.0 m, how much sound power does that person generate? • The power output of a tuba is 0.35 W. At what distance is the sound intensity of the tuba 1.2 x 10-3W/m2?

10. The Doppler Effect • The shift in perceived frequency of a wave due to relative motion between the source and the observer. • Observable in both sound (pitch) and light (red and blue shifts) • As the sound approaches - higher f • As sound leaves - lower f • Occurs as either listener or source is moving

11. Forced Vibrations and Natural Frequency • Forced Vibration – a vibration that occurs when a periodic force causes an object to vibrate at a particular frequency • Singing • Natural Frequency – the frequency an object will vibrate at when given a one time force • Depends on shape and material of object

12. Resonance • The amplified wave that occurs when a forced vibration on an object matches the natural frequency of the object. • Makes the wave progressively larger. • Swing set example

13. Music • Different notes have different mathematical relationships between their frequencies. • Specific frequency combinations are considered pleasant (harmony) and others unpleasant (dissonance). • 2:1 = Octave (C to the next C) • 5:4 = Major Third (C to E) • 4:3 = Perfect Forth (C to F) • 3:2 = Perfect Fifth (C to G)

14. Instruments • The sound produced by the vibration of a piece of the instrument (string, reed, lips) is amplified and shaped through resonance by the rest of the instrument. • Standing waves are produced within the instrument at certain frequencies depending on either the properties of the string or the shape and size of the instrument.

15. Strings • Physically, wavelength is restricted to certain values. • To change those values, the length of the string needs to be changed (different keys on a piano, different finger placements on a guitar) • The longest wavelength on the string is the sound you hear as the note being played and is called the fundamental or first harmonic.

16. Wavelengths • The higher frequency vibrations are played simultaneously and are called overtones. Therefore, the next longest wavelength will be the second harmonic or first overtone.

17. Frequencies • Since all of the waves are on the same medium and travel at the same speed, there will be a pattern to the frequency as well as the wavelength.

18. Closed Pipe • Node on one end, antinode on the other. • Diagrams help with determining wavelength pattern.

19. Wavelengths and Frequencies • Where n=1, 3, 5… • Closed pipes have only odd harmonics

20. Open Pipes • The same as the closed pipe, however there is an anti-node at each end for molecular movement and a node at each end for pressure variance.

21. Wavelengths and Frequencies

22. Beats • Beats are a result of two waves with close, but not identical frequencies. • A pattern of constructive and destructive interference forms creating a warbling sound. • Useful for tuning instruments. • Beat frequency is equal to the difference between the two component frequencies.

23. Timbre • The unique combination of intensities of fundamental and overtone frequencies that makes instruments sound different when playing the same note. Trumpet Flute Cello

24. Examples • What is the fundamental frequency of a 0.2 m long organ pipe that is closed at one end, when the speed of sound in the pipe is 352 m/s? • A flute is an open pipe. The length is the flute is approximately 66.0 cm. What are the first three harmonics of a flute when all keys are closed, making the length of air equal to the length of the flute? Use 340 m/s for the speed of sound. • What is the fundamental frequency of a guitar string when the speed of waves on the string is 115 m/s and the effective string lengths are as follows: • 70.0 cm • 50.0 cm • 40.0 cm • A violin string that is 50.0 cm in length has a fundamental frequency of 440 Hz. What is the speed of the waves on this string?