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Understanding Sound: Vibrations, Waves, and Interference in Music and Instruments

Explore the principles of sound through vibrating strings and air columns, interference of sound waves, Doppler effect in music, and more. Learn how instruments produce different sounds and frequencies. Discover the science behind why trumpets and flutes sound distinct. Delve into the quality of sound, overtones, and beats. Dive into problems and examples on resonating pipes, harmonics, fundamental frequencies, and wave phenomena. Unravel the mysteries of sound waves with detailed explanations and illustrations.

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Understanding Sound: Vibrations, Waves, and Interference in Music and Instruments

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  1. Chapter 16: Sound HW2: Chapter 16: Pb.2, Pb 18, Pb.24, Pb 35, Pb.40, Pb.62 Due on Wednesday 24.

  2. Problem 39 39. (II) An unfingered guitar string is 0.73 m long and is tuned to play E above middle C (330 Hz). (a) How far from the end of this string must a fret (and your finger) be placed to play A above middle C (440 Hz)? (b) What is the wavelength on the string of this 440-Hz wave? (c) What are the frequency and wavelength of the sound wave produced in air at 25°C by this fingered string?

  3. 16-4 Sources of Sound: Vibrating Strings and Air Columns A tube openat both ends (most wind instruments) has pressure nodes, and therefore displacement antinodes, at the ends.

  4. 16-4 Sources of Sound: Vibrating Strings and Air Columns A tube closedat one end (some organ pipes) has a displacement node(and pressure antinode) at the closed end.

  5. 16-4 Sources of Sound: Vibrating Strings and Air Columns Example 16-10: Organ pipes. What will be the fundamental frequency and first three overtones for a 26-cm-long organ pipe at 20°C if it is (a) open and (b) closed?

  6. Problem 35 35. (I) An organ pipe is 124 cm long. Determine the fundamental and first three audible overtones if the pipe is (a) closed at one end, and (b) open at both ends.

  7. Problem 44 44. (II) A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed pipe. (b) What is the fundamental frequency of this pipe?

  8. Problem 46 46. (II) A uniform narrow tube 1.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is (a) the fundamental frequency, and (b) the speed of sound in the gas in the tube?

  9. 16-4 Sources of Sound: Vibrating Strings and Air Columns Wind instruments create sound through standing waves in a column of air. The lip of the player will set up the vibrations of the air column. In a uniform narrow tube such as a flute or an organ pipe, the shape of the waves are simple.

  10. 16-5 Quality of Sound, and Noise; Superposition So why does a trumpet sound different from a flute? The answer lies in overtones —which ones are present, and how strong they are, makes a big difference. The sound wave is the superposition of the fundamental and all the harmonics.

  11. 16-6 Interference of Sound Waves; Beats • Sound waves interferein the same way that other waves do in space. The difference BE has to be n(1/2)λof the sound for destructive interference to occur

  12. 16-6 Interference of Sound Waves; Beats Sound Waves can also interfere in time,causing a phenomenon calledbeats. Beats are the slow “envelope” around two waves that are relatively close in frequency.

  13. 16-6 Interference of Sound Waves; Beats • If we consider two waves of the same amplitude and phase, with different frequencies, we can find the beat frequency when we add them: • This represents a wave vibrating at the average frequency, with an “envelope” at the difference of the frequencies. • The beat frequency is the difference in the two frequencies.

  14. 16-6 Interference of Sound Waves; Beats Example 16-12: Loudspeakers’ interference. Two loudspeakers are 1.00 m apart. A person stands 4.00 m from one speaker. How far must this person be from the second speaker to detect destructive interference when the speakers emit an 1150-Hz sound? Assume the temperature is 20°C. BE =n(1/2)λ

  15. 16-6 Interference of Sound Waves; Beats • Example 16-13: Beats. • A tuning fork produces a steady 400-Hz tone. When this tuning fork is struck and held near a vibrating guitar string, twenty beats are counted in five seconds. What are the possible frequencies produced by the guitar string?

  16. Problem 54 54. (I) What is the beat frequency if middle C (262 Hz) and (277 Hz) are played together? What if each is played two octaves lower (each frequency reduced by a factor of 4)?

  17. 16-7 Doppler Effect https://www.youtube.com/watch?v=h4OnBYrbCjY

  18. 16-7 Doppler Effect • TheDoppler effectoccurs when a sourceof sound is movingwith respect to an observer. • A source moving towardan observer appears to have a higherfrequency and shorterwavelength; a source moving awayfrom an observer appears to have a lowerfrequency and longerwavelength.

  19. 16-7 Doppler Effect • The change in the frequencyis given by: • If the source is moving toward the observer • If the source is moving away from the observer:

  20. 16-7 Doppler Effect • If the observeris moving with respect to the source, things are a bit different. The wavelengthremains the same, but the wave speedis different for the observer.

  21. 16-7 Doppler Effect • We find, for an observer moving toward a stationary source: • And if the observer is moving away:

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