Sound Sound waves are –Longitudinal –Pressure Waves Infrasonic – less than 20 Hz Audible – between 20 and 20,000 Hz Ultrasonic – greater than 20,000 Hz Frequency – tone Amplitude – volume

Sound waves are mechanical waves, which means the wave needs a medium to travel through. (This is why there is no sound in space, there is no air for the sound wave to propagate through) Sound waves are traveling pressure waves. They are packets of low and high pressure regions which are picked up by your eardrums and interpreted as sounds in your brain.

Fig. 17.1, p.513

Fig. 17.2, p.515

Speed of Sound In air (at 20 o C) = 343 m/s In air (at temp = T in Kelvin)

Speed of Sound In a fluid or gas - depends on the density of the medium and the Bulk Modulus (ch. 9) In a solid - depends on the density of the medium and the Young’s Modulus (ch. 9)

Table 17.1, p.514

Intensity of Sound The average intensity of a wave is defined as the rate at which energy flows through a surface area.

Decibel Level It makes more sense to talk about sound intensity in terms of decibels. Units: dB (decibel) I o =1.0 x W/m 2 (this is the reference intensity – the sound intensity at the threshold of hearing)

Table 17.2, p.520

Fig. 17.6, p.521

Examples A vacuum cleaner has a measured sound intensity of 70 dB. Calculate the intensity of the sound:

Examples A loud rock band produces a sound level of 120 dB right in the middle of the band. The sound intensity there is:

Spherical and Plane Waves Sound waves are spherical waves

Doppler Effect Sound waves are spherical waves. This means that depending on your position and motion (relative to the source of the sound) the sound you hear will differ. This effect is called the Doppler Effect. If neither the source nor the observer are moving, then the sound heard by the observer will not be altered. But if either the source or the observer (or both!) are moving relative to each other, then there will be a Doppler shift in the frequency (tone) of the sound.

Examples A train blows its whistle as it approaches and you hear a frequency of 510 Hz. When the train stops and blows its whistle again, the frequency that you hear is 490 Hz. Find the speed at which the train was approaching.

Examples A train is moving parallel to a highway with a constant speed of 20 m/s. A car is traveling in the same direction as the train with a speed of 40 m/s. The train whistle sounds at a frequency of 320 Hz. If the car is behind the train, the frequency (in Hz) of the train whistle that the car driver hears is:

Sound Wave Interference Path difference = |r 2 - r 1 | When the path difference is an integer multiple of the wavelength of the sound, there is constructive interference When the path difference is a half-integer multiple of the wavelength of the sound, there is destructive interference

Waves on a String There are only certain stable patterns that will occur on a particular sting. These are called the normal modes of oscillation. The properties of the spring ( , L, T) determine the normal modes of oscillation. The motion of the string at one of these normal modes of oscillation is a standing wave. If the spring is driven at a frequency that is not one of the normal frequencies, then the string will not exhibit a stable pattern.

Standing Waves - string

Standing Wave - string terminology n = 1Fundamental1 st harmonic n = 2First overtone2 nd harmonic n = 3Second overtone 3 rd harmonic n = 4Third overtone4 th harmonic

Standing Waves - string We can look at the standing wave patterns to determine a relationship between L and. Fundamental 2 nd harmonic 3 rd harmonic nth harmonic

Standing Waves - string Rearrange that last equation: and since v=f  Replace the velocity of a wave on a string with the equation from last chapter,

Resonance All of the possible harmonic frequencies are also called resonance frequencies. If you add energy to the system at a frequency equal to one of the resonance frequencies, you will continually add to the amplitude of the vibration (motion) of the system. Eventually, the system will break. Exs: Tacoma Narrows Bridge, a shattered wine glass (from a high note).

Standing Waves - pipe There are particular harmonics for sound waves in pipes. At each of the harmonics, the pipes produce a “clean” sound. The harmonics are dependent on the length of the pipe.

Standing Waves – open pipe

Standing Wave – open pipe terminology n = 1Fundamental1 st harmonic n = 2First overtone2 nd harmonic n = 3Second overtone 3 rd harmonic n = 4Third overtone4 th harmonic

Standing Waves – closed pipe

Standing Wave – closed pipe terminology n = 1Fundamental1 st harmonic n = 3First overtone3 rd harmonic n = 5Second overtone 5 th harmonic n = 7Third overtone7 th harmonic

Beats

Examples A music pipe that is open at both ends has a fundamental frequency of 512 Hz. The length of the pipe in meters is:

Examples A violin string 30 cm long and of mass kg, is under a tension of 800 N. What is the wavelength and frequency of the fundamental mode for the standing waves?

Examples An organ pipe, closed at one end and open at the other, is 32 cm long. What is the wavelength and the frequency of the fundamental mode for the standing waves?