Sound

1. Sound Unit 8

2. What is sound? How do we perceive sound?

3. Sound • Sound is a longitudinal wave. • We most commonly experience sound waves traveling through air. • However, sound can travel through any type of matter. • We detect sound using our ears or a microphone.

4. Speed of Sound • Because sound is the longitudinal vibration of matter, sound waves require matter to travel. • Sound waves cannot travel through space. • The speed of the sound wave depends on the material the wave is traveling through (much the same way the speed of mechanical waves depended on the properties of the string).

5. Speed of Sound • The speed of sound also depends on temperature. • For our purposes, we will assume that our sound waves are traveling through air at 20° C. • In this case, the speed of sound is 343 m/s.

6. Vocabulary of Sound • There are many common terms associated with sound in our every day lives. • The loudness of sound is related to the intensity of the sound wave (more on this in a minute. • The pitch of a sound refers to how high (like a piccolo) or low (like a bass) a sound is.

7. Vocabulary of Sound • The pitch is determined by the frequency of the sound wave. • A human ear can detect frequencies ranging from 20 Hz to 20,000 Hz. This is known as the audible range. • Sounds with frequencies above the audible range are called ultrasonic. • Sounds will frequencies below the audible range are called infrasonic.

8. Pressure Waves • In the last unit, we described waves in terms of the oscillations of the particles making up the medium. • While sound waves can be described this way, it’s often difficult to measure the displacement of air molecules.

9. Pressure Waves • Instead, we analyze sound waves by looking at pressure. • When the molecules are closer together, the pressure is greater.

10. Intensity of Sound Decibels

11. Intensity of Sound • We experience the intensity of sound through loudness. • Recall that intensity is a measure of the power delivered by a wave over a given area. • Intensity is measured in W/m2.

12. Intensity of Sound • The human ear can detect a wide range of intensities. • However, what we perceive as loudness is not actually proportional to the intensity of the sound. • To produce a sound that is twice as loud requires a wave that has about 10 times the intensity.

13. Decibels • Because of this relationship between loudness and intensity, sound intensity levels are described using a logarithmic scale. • The unit of this scale is a bel, though the related decibel is much more commonly used.

14. Decibels • The sound level (loudness) of any sound is defined in terms of the intensity by: • Here, I0 is the intensity of a chosen reference level.

15. Decibels • Generally, we pick I0as the threshold of hearing for a good ear: • So, for example, if we had a sound with intensity I = 1.0 x 10-10.

16. Example: Sound on the Street At a busy street corner, the sound level is 70 dB. What is the intensity of sound there?

17. Example: Loudspeaker

18. Homework • Read 12-1 and 12-2. • Do problems 3, 5, 9, and 11 on page 347.

19. Announcements • If you own a (portable) musical instrument, please come talk to me after class today. • There will be a daily exercise quiz on Friday

20. Sources of Sound

21. Sources of Sound • Sound is generated by any object that is vibrating in a medium (such as air). • While almost any object can be a source of sound, most are very difficult to analyze. • Today, we will be looking at one of the most common sources of sound: musical instruments.

22. Sources of Sound • There are two main types of musical instruments: • For a string instrument, standing waves are produced when the string is plucked or bowed. This generates sound waves of the same frequency. • For a wind instrument, vibrating columns of air produce standing waves within the instrument.

23. String Instruments • We saw last unit how standing waves can be established on a string. • When a string is plucked the wave that results is actually a superposition of standing waves. • The dominant pitch that is heard corresponds to the fundamental frequency. • However, there are overtones corresponding to higher frequencies as well.

24. String Instruments • Recall from last unit that the fundamental frequency is given by: • Where v is found using

25. String Instruments • The pitch of many string instruments can be controlled by placing a finger on the string. • When this happens the effective length of the string is shortened. • This results in a change in the frequency of vibration (since L has changed but v has not).

26. Example: Violin A 0.32 m long violin is tuned to play the A above middle C at 440 Hz. a) What is the wavelength of the standing wave on the string that corresponds to this note? b) What are the frequency and wavelength of the resulting sound wave? c) Why is there a difference?

27. Example: Piano Strings The highest key on a piano corresponds to a frequency that is 150 times the frequency of the lowest key. If the string for the highest note is 5 cm long, how long would the string for the lowest note have to be if it had the same mass per unit length and was under the same tension? Based on your answer, can you explain why the strings for the low notes of a piano are heavier than those for the high notes.

28. Wind Instruments • Wind instruments produce sound from standing compression waves in a column of air. • This standing wave is initiated by a vibration in a reed on a person’s lips. • Sometimes the vibration is generated by directing a stream of air against one edge of the opening of the tube.

29. Wind Instruments • A string vibrating at the fundamental frequency has a node at either end. • The result is similar for wind instruments. • However, now it is the air itself that is vibrating to cause the sound.

30. Wind Instruments • There are two types of wind instruments. • An open tube, where there is an opening at either end of the tube. • A closed tube, where one end of the tube is blocked. • In both cases, we can describe the wave in terms of either displacement or pressure.

31. Open Tubes • In an open tube, the air molecules vibrate horizontally. • Since the air is free to move at both ends, there will always be displacement antinodes at either end of the tube.

32. Open Tubes • Since there must be at least one node to form a standing wave, the fundamental frequency corresponds to one displacement node. • This corresponds to two nodes and one antinode for the pressure wave (just like the string).

33. Open Tubes • Looking at the pressure wave, we can see that λ1 = 2L. So,

34. Closed Tubes • In an closed tube, the air molecules also vibrate horizontally. • However, now air is only free to vibrate at one end. This creates a displacement node at the closed end. And an antinode at the other.

35. Closed Tubes • Based on this, we can see that λ1 = 2L. So, • Which is half the result for the open tube.

36. Closed Tubes • However, there is a second difference. Because the open end must have an antinode, only odd harmonics are allowed. Thus

37. Example: Organ Pipes What will be the fundamental frequency and first three overtones for a 26 cm long organ pipe if the pipe is a) open, and b) closed?

38. Homework • Read 12-4. • Do problems 25, 28, 29 on page 348. • For problem 29, refer to the table at the beginning of section 12-4.

39. Problem Day • Do problems 26, 27, 33, and 34 on page 348. • We will whiteboard these at 3:30.

40. Homework • Do problems 35, 36, and 37 on page 348.

41. Whiteboarding Groups

42. Quality of Sound

43. Quality of Sound • Whenever we hear a sound, we are always aware of its loudness and its pitch. • However, we are also aware of a third aspect called the “quality” of the sound. • An example of this can be found in instruments: a piano, a clarinet, and a human voice can all produce the same note. However, the sounds are clearly different.

44. Quality of Sound • The quality of a sound is that which allows us to tell the difference between instruments or other sources of sound. • In music, the terms timbre and tone color are also used. • Like loudness and pitch, quality can be related to a physical characteristic of the sound wave.

45. Quality of Sound • The quality of a sound depends on the number of overtones that are present and the amplitude of each overtone. • When a note is played on an instrument, the fundamental frequency and several overtones are present simultaneously.

46. Quality of Sound • These waves all get added together through the principle of superposition to produce the sound we actually hear. • However, each overtone has a different amplitude (usually smaller than that of the fundamental).

47. Quality of Sound • The relative amplitudes for the overtones are different for each instrument. • The differences in amplitude produce different composite waveforms for each instrument, giving each a unique sound.

48. Sound Spectrum • It is possible to identify the different frequencies that make up a waveform along with the relative amplitude of each frequency. • This process is called a Fourier transform. (you won’t be required to know how to do this)

49. Sound Spectrum • Through a Fourier transform, a bar graph showing the amplitude of each frequency that makes up a sound can be generated. • This graph is called the sound spectrum. • The fundamental frequency is generally the loudest (has the greatest amplitude) and is therefore what is heard as the pitch.

50. Sound Spectrum • Sound spectra for different instruments. The spectrum changes depending on the note being played. • The clarinet acts as closed tube (odd harmonics only) at low frequencies and an open tube (all harmonics) at high frequencies.