Calculate the speed of 25 cm ripples passing through water at 120 waves/s

Determine the, f, & T of the 49 th overtone of a 4.0 m organ pipe when v sound = m/s

Chapter 15 Sound

Sound Waves Longitudinal waves caused by pressure change producing compressions & rarefactions of particles in the medium

Sound Waves Any vibrations produce regular oscillations pressure as the vibrating substance pushes air molecules back & forth

Sound Waves The oscillating air molecule collide with others transmitting the pressure variations away from the source

Sound Waves Air resistance will cause the amplitude of the wave to diminish as it moves away from the source

Speed of Sound v sound in air = m/s + (0.60 m/s o C)(T)

Speed of Sound v sound ~ 343 m/s At room temp.

Speed of Sound at 25 o C v in air = 343 m/s v fresh water = 1493 m/s v sea water = 1533 m/s v in steel = 5130 m/s

The human ear can detect sound between 20 Hz & 16 kHz. Calculate the wavelength of each:

Calculate the in mm of notes with frequencies of: 2.0 kHz & 10.0 kHz v sound = 342 m/s

Loudness How loud sound is, is proportional to the amplitude of its waves

Decibels (dB) Unit for measuring the loudness of a sound wave

Decibels Measured in log units 50 dB is 10 x greater than 40 dB

Pitch Pitch is proportional to the frequency or inversely proportioned to the wavelength

Doppler Effect Changes in observed pitch due to relative motion between the source & the observer of the sound wave

Doppler Effect The pitch of approaching objects has higher frequencies or shorter wavelengths

Doppler Effect The pitch of objects moving apart has lower frequencies or longer wavelengths

The Physics of Music

Almost all musical instruments are some form of an open tube or strings attached at two ends

In brass instruments, the lip vibrates against the mouthpiece causing the instrument to vibrate

In reed instruments, air moving over the reed causes it to vibrate causing the instrument to vibrate

In pipe instruments, air moving over the opening causes air to vibrate causing the instrument to vibrate

In stringed instruments, plucking the string causes it to vibrate causing the instrument to vibrate

In musical instruments, the sound is dependent upon resonance in air columns

In each instrument, the longest wavelength produced is twice the length of string or air column

Resonance When multiple objects vibrate at the same frequency or wavelength

Resonance Resonance increases amplitude or loudness as multiple sources reinforce the waves

Resonance The length & width of the air column determine the pitch (frequency or wavelength)

Resonance In instruments sound resonates at a fundamental pitch and many overtones

Calculate the wavelengths for each of the following sound frequencies at o C: 4.0 MHz & 10.0 MHz

Fundamental The lowest tone or frequency that can be generated by an instrument

Overtones Sound waves of higher frequency or pitch than the fundamental

Pipe Resonance Open Pipe: open at both ends Closed Pipe: Closed at one end

Pipe: Open End High Pressure-antinode Zero Displacement- node

Pipe: Closed End Pressure node Displacement antinode

Closed Pipe Resonator A pipe that is closed at one end

Open Pipe Resonator A pipe that is open at both ends

Wavelengths Generated by a Closed Pipe Resonator = 4L/(2n +1) f = v(2n+1)/4L

Wavelengths Generated by a Closed Pipe Resonator n = 0 for the fundamental

Wavelengths Generated by a Closed Pipe Resonator n = positive integers for overtones

Typical Wavelengths Generated by CP 0 = 4L 1 = 4L/3 2 = 4L/5

Wavelengths Generated by an Open Pipe Resonator = 2L/(n+1) f = (n+1)v/2L

Wavelengths Generated by an Open Pipe Resonator n = 0 for the fundamental

Wavelengths Generated by an Open Pipe Resonator n = positive integers for overtones

Typical Wavelengths Generated by OP 0 = 2L 1 = 2L/2 2 = 2L/3

Calculate the longest wavelength & the first two overtones produced using a 68.6 cm saxophone. (open)

Calculate the wavelengths & frequencies of the longest & the first 4 overtones produced using a 2.0 m tuba.

Calculate the wavelengths & frequencies of the lowest & the first 4 overtones produced using a 5.0 cm whistle. (closed)

Sound Quality

Fundamental The lowest tone or frequency that can be generated by an instrument

Overtones Sound waves of a higher frequency or pitch than the fundamental

Harmonics Sound waves of higher frequency or pitch than the fundamental or overtones

Timbre Quality of sound Addition of all harmonics generated determines timbre

Beat Oscillations in sound wave amplitude Can be produced by wave reinforcement

Consonance Several pitches produced simultaneously producing a pleasant sound called a: Chord

Dissonance Several pitches produced simultaneously producing an unpleasant sound or: Dischord

Consonance Consonance occurs when the frequencies having small whole number ratios

Consonance Frequency Ratios 2:3 3:4 4:5

Consonance Frequency Ratios The notes in the chord C major have frequency ratios of 4:5:6

Octave When two notes with a frequency ratio of 2:1, the higher note is one octave above the lower note

Frequency Ratios 1:2 - octave 2:3 - Perfect Fifth 3:4 - Perfect Fourth 4:5 - Major Third

Noise A mixture of a large number of unrelated frequencies

Determine the, f, & T of the 19 th overtone of a 50.0 cm open tube when v sound = m/s

Determine the, f, & T of the 9 th & 14 th overtone of a 80.0 cm open tube when v sound = m/s

Determine the, f, & T of the fundamental & 1 st three overtones of a mm open tube when v sound = m/s