Chapter 18 WAVES  II 18.1 Sound Waves A sound wave in air is a longitudinal wave. The restoring force for such a wave is due to the pressure of air.

The frequencies of audible sound is in the range from 20 to 20,000 Hz The frequencies of audible sound is in the range from 20 to 20,000 Hz. Frequencies above 20,000 Hz are called ultrasound and frequencies below 20 Hz are called infrasound. The intensity of a sound wave is the power transported by this wave per square meter of wave front; the units of intensity are W/m2. Threshold of hearing: At a frequency of 103 Hz, the minimum intensity audible to the human ear is 1.21012 W/m2.

Intensity level: the intensity of sound in a logarithmic scale. The unit of intensity level is the decibel (dB); we take an intensity of 0.4681012 W/m2 as our standard of intensity: The threshold of hearing(1.21012 W/m2) corresponds to 4 dB and the threshold of pain (1 W/m2) corresponds to 120 dB.

Sound Intensity level Rupture of eardrum 160 dB Jet engine (at 30 m) 130 Threshold of pain 120 Rock music 115 Thunder (loud) 110 Subway train (New York City) 100 Heavy street traffic 70 Normal conversation 60 Whisper 20 Normal breathing 10 Threshold of hearing 4

According to Fourier’s theorem, a sound wave of arbitrary shape can be regarded as a superposition of harmonic waves. The relative intensity of the harmonic waves in this superposition determines the timbre (or quality) of the sound. White noise, consists of a mixture of harmonic waves of all frequencies with equal intensities. The musical notes emitted by a piano or a violin consist of a mixture of just a few harmonic waves.

Note Frequency C 261.7 Hz C# 277.2 D 293.7 D# 311.2 E 329.7 F 349.2 F# 370.0 G 392.0 G# 415.3 A 440.0 A# 466.2 B 493.0

Middle C: 261.7 Hz C one octave above: 523.3 Hz C two octaves above: 1046.6 Hz

18.2 The Speed of Sound v = 331 m/s The speed of sound For the speed of sound in the condition of temperature 0 C, po = 1 atm = 1.01105 N/m2, and o = 1.29 kg/m3 v = 331 m/s

Material v Air 0 º C , 1atm 311 m/s 20 º C , 1atm 344 100 º C , 1atm 386 Helium, 0 º C , 1atm 965 Water (distilled) 1497 Water (sea) 1531 Aluminum 5104 Iron 5130 Glass 5000-6000 Granite 6000

The measurement of the speed of sound in air:

The wavelengths of the normal modes Eigenfrequencies In general,

18.3 The Doppler Effect 18.3.1 Moving observers, source at rest If an observer is moving toward a wave source, he will receive more numbers of wave in a unit time, vO /. Thus, the number of received waves in a unit time is

In the case of an observer moves away from a source, the frequency he receives is In together, if an observer is moving toward to and away from the source, the frequency received is

18.3.2 Moving source, observer at rest When the source is in motion toward a stationary observer, the effect is a shorten of the wavelength. The wavelength the observer receives is The frequency is

In an opposite case in which the wave source is moving away from the observer, the measured frequency is In general, when the source in motion along the line of source and observer, the frequency observed by a stationary observer is In both source and observer move through the transmitting medium

18.4 Supersonic Speeds: Shock Waves If a source is moving toward a stationary detector at a speed equal to the speed of sound, we can predict that the detected frequency will be infinitely great.

When the speed of the source exceeds the speed of sound, it is called a shock wave. The Mach cone: The Mach number:

A photograph of a projectile fired from a gun at Mach 2.

Problems: 1. 18-4 (on page 421), 2. 18-29, 3. 18-33, 4. 18-49, 5. 18-51, 6. 18-59.