PHY238Y Lecture 8  Sound waves  The speed of sound  Traveling sound waves  Intensity and sound level References: Haliday, Resnick, Walker: Fundamentals of Physics, 6 th ed., Wiley 2003, Ch. 18 (18.1 – 18.3, 18.5) Hallett et al.: Physics for the life sciences, 4 th ed., Ch.2 (2.1 – 2.5) Thanks to dr. R. Nave for the permission to use some of the pictures from Hyper Physics:

PHY238Y Lecture 8 Sound waves are longitudinal A single-frequency sound wave traveling through air will cause a sinusoidal pressure variation in the air. The air motion which accompanies the passage of the sound wave will be back and forth in the direction of the propagation of the sound.

PHY238Y Lecture 8 The elastic property of a gas or liquid is called bulk modulus The speed of sound:

PHY238Y Lecture 8 Sound pressure: Audible sound consists of pressure waves  Sound pressure p m is defined as the amplitude of the pressure wave  The power carried by the wave is proportional to the square of the amplitude

PHY238Y Lecture 8 Traveling sound waves:  Displacement and pressure variations

PHY238Y Lecture 8 Sound intensity is Power/unit area or: time rate of energy transfer/unit area  Many sound intensity measurements are made relative to a standard threshold of hearing intensity I 0,  The most common approach to sound intensity measurement is to measure the sound level on the decibel scale: The factor of 10 multiplying the logarithm makes it decibels instead of Bels, and is included because ~ 1 decibel is the just noticeable difference (JND) in sound intensity for the normal human ear

PHY238Y Lecture 8 The threshold of hearing  The measured threshold of hearing curve shows that the sound intensity required to be heard is quite different for different frequencies.  The standard threshold of hearing at 1000 Hz is nominally taken to be 0 dB (it actually is 4 dB)

PHY238Y Lecture 8 Threshold of pain is 120 – 130 dB The dynamic range of human hearing extends from zero dB to the threshold of pain. Example: problem 18-2 p. 404 from Halliday/Resnick/Walker Intensity level (dB) Ear drum rupture160 Pain threshold Shotgun blast100 Car horn (6 m distance) 90 City street75 Typical room40 Open country10 Threshold of hearing 0

PHY238Y Lecture 8 The audible sound: a pressure wave with frequency between 20 Hz and 20,000 Hz and with an intensity above the standard threshold of hearing: Frequency: 20 Hz - 20,000 Hz (corresponds with pitch) Wavelength (at 20 o C in air): m – 17.2 m Intensity: W/m 2 (0 to 130 dB) Pressure: 2 x N/m 2 (2 x atm) Sounds may be generally characterized by:  Pitch (frequency)  Loudness (is NOT simply the intensity level)  Quality (timbre – determined by the harmonic content of the sound)

PHY238Y Lecture 8 Variation of intensity with distance: the inverse square law:

PHY238Y Lecture 8 Inverse square law plot