Unit 1: Waves Lesson: Sound Sound is a mechanical wave, a longitudinal wave, a pressure wave Periodic sound waves have: Frequency f determined by the source of vibration; related to pitch of sound Period T time taken for one complete vibrational cycle Wavelength λ smallest distance between any two corresponding points on the wave Wave speed v determined by the material Amplitude A maximum change in pressure - determines loudness of sound Frequency of Sound: Audible: within range of human hearing 20 Hz f 20,000 Hz; upper limit decreases with age. Infrasonic: low frequency, below range of human hearing f 20 Hz - Elephants, whales, earthquakes, pipe organs, giraffes Ultrasonic: high frequency sound, above range of human hearing f 20,000 Hz - Dog whistle, bats, medical imaging, cleaning devices Within the audible range, the frequency of a sound determines its pitch. Higher frequency = higher pitch, lower frequency = lower pitch Certain pitches (or frequencies) may be named C = 256 Hz A = 440 Hz 1
Speed of Sound: determined by elastic and inertial properties of the medium. (Elastic properties are those properties related to the tendency of a material to maintain its shape and not deform whenever a force or stress is applied to it. Inertial properties are those properties related to the material's tendency to be sluggish to changes in its state of motion. The density of a medium is an example of an inertial property). v solid v liquid v gas At 20 C, speed of sound in air = 343 m/s water = 1490 m/s iron = 5130 m/s In air, the speed of sound increases slightly with an increase in temperature at 0 C, v = 331.5 m/s at 20 C, v = 343 m/s Equation for speed of sound in air (at temperature T C ) ( ) ( ) ( ) Example: Calculate the wavelength of sound produced by a tuning fork of pitch C. Example: Calculate the speed of sound at 39 C. Amplitude of Sound: Loudness of a sound wave is determined by its amplitude. The human ear is sensitive to a huge range of intensities. 2
Since this range is so large, it is convenient to define a logarithmic scale for use in discussing sound loudness. An increase of 1 on this scale corresponds to vibrations with amplitudes 10 times as large and about 30 times as much energy other logarithmic scales ph scale Richter scale At threshold of hearing β = 0 db At threshold of pain β = 120 db 60 db 10 times as loud as 50 db 70 db 100 times as loud as 50 db Doppler Effect The Doppler effect is observed whenever the source of waves is moving with respect to an observer. There is an apparent upward shift in frequency for observers towards whom the source is approaching, and an apparent downward shift in frequency for observers from whom the source is receding. http://www.astro.ubc.ca/~scharein/a311/sim/doppler/doppler.html 3
It is important to note that the effect does not result because of an actual change in the frequency of the source. f s = source frequency f / = doppler-shifted frequency v = speed of sound (343 m/s at room temp.) v d = speed of detector (or observer) v s = speed of source ( ) Example: A detector moves toward a source of sound of 512 Hz at a speed of 45 m/s. What is the perceived frequency? Beats and beat frequency: When two sound waves of slightly different frequencies interfere, they produce sound with oscillating amplitude or loudness. The frequency of this oscillation is Ex: two tuning forks, tuning a piano string 4
Sound quality Different musical produce sounds of different quality (or timbre) due to non-sinusoidal wave patterns. The musical note is the sum of a fundamental frequency and higher harmonics. Resonance and Standing Waves: Natural frequency: The frequency or frequencies at which an object tends to vibrate with when struck (or disturbed). Forced vibration: an object forces another adjoining or interconnected object into vibrational motion. Resonance: When two interconnected objects share the same vibrational frequency, resonance occurs. The resulting vibration is large. Ex: Resonance apparatus in lab: When the natural frequency of the air column is tuned to the frequency of the vibrating tuning fork, resonance occurs, and you hear a loud sound. Standing wave pattern: vibrational pattern created within a medium when the vibrational frequency of the source causes reflected waves from one end of the medium to interfere with incident waves from the source. Standing sound waves: Created when 2 identical periodic sound waves moving in opposite directions interfere. 5
Antinodes large amplitude oscillation loud Standing waves produced in a tube or a column of air, open at both ends: Standing waves produced in a closed tube, or a column of air (ie. open only at one end): 6
End correction: When resonance exists, the displacement is a minimum (node) at the closed end, but the antinode is not exactly at the open end. It is actually a small distance beyond it. This extra distance beyond the end of the tube is called the end correction. The end correction depends primarily on the radius of the tube: it is approximately equal 0.3 times the diameter. Wavelength of standing wave in resonating air column with end-correction: λ is the wavelength of the sound wave L is the length of the air column d is the diameter of the tube: Example: Using a 256 Hz tuning fork you hold it over a 2.5 cm diameter tube that is in a container of water. By moving the tube up and down you are able to produce resonance when the air column in the tube is 32 cm long. Based on this information determine the temperature of the air that day to the nearest whole degree. 7