Sound

1. Sound Chapter 17

2. Wave fronts In a flat region of space, spherical wave fronts are near planar

3. Longitudinal waves consist of zones of high and low frequency Octave Musical notes that differ by a factor of 2 in frequency are separated by an octave Ultrasound Sound waves above normal human hearing range (>20000Hz)

4. Intensity of Sound I = P/A Intensity is expressed on a logarithmic scale, (dB) decibel Intensity level in dB = (10dB) x log10)

5. Example • Express the threshhold of hearing (2.5 x 10-12 W/m2) and the threshhold of pain (1.0 W/m2) in decibels. Solution: (10dB)x log10 (2.5x 10-12W/m2) = (10dB) x log10(2.5) = 4.0 dB 1.0x 10-12 W/m2 (10dB)x log10 (1.0 W/m2) = (10dB) x log101012) = 120 dB 1.0x 10-12 W/m2

6. As a sound wave spreads out from it source, its intensity falls off because the area of the wavelength grows larger; the wave energy per unit area grows smaller and

7. At a distance of 30m from a jet engine, the intensity of sound is 10W/m 2 , and the intensity level of 130dB. What are the intensity and intensity level at a distance of 180dB? I 2 = r12 I1 = (30m)2 I1 = (2.8 x 10-2) x I1 = (2.8 x 10-2) x (10W/m2) = 2.8 W/m2 r22 (180m)2 (10dB)x log10(0.28W/m2) = (10dB) x log10(0.28 x1012) = 114 dB 1.0x 10-12 W/m2

8. The Speed of Sound : Standing Waves • Speed of sound (in air, 0⁰C, 1 atm) = 331 m/s

9. The standing sound wave in the column of air in a tube closed at one end must have a displacement node at the closed end and and antinode at the open end Only odd multiples are possible λ1= 4L, λ2 = 4/3L, λ3 = 4/5L, λ4 = 7/4L, … Eigenfrequencies: (f = v/ λ) f1 = v/4L, f2 = 3v/4L, f3 = 5v/4L, …

10. A tube open at both ends: eigenfrequencies

11. The Doppler Shift http://www.astro.sunysb.edu/mzingale/software/astro/doppler.avi A receiver will detect a higher frequency when the source is approaching, and a lower frequency when the source is moving away from the receiver. Doppler shift, moving receiver f’/ f = v’/v f’ = f(1 ± VR/v)

12. Example: Suppose that a stationary siren emits a tone of frequency 440 Hz as the train moves away from it at 30.0m/s. What is the frequency received on the train? A motorboat speeding at 6.0 m/s is moving in the same direction as a group of water waves of frequency 0.62 Hz and speed 2.5 m/s (relative to the water). What is the frequency with which the wave crests pound on the motorboat? f’ = f(1 - VR/v) f’ = 440Hz(1 – 30 m/s/331 m/s)= 400Hz f’ = f(1 - VR/v) f’ = 0.62Hz(1 – 6.0m/s/2.5 m/s)= -0.87Hz

13. Doppler shift, moving emitter f’ Example: Suppose that a stationary siren emits a tone of frequency 440 Hz as the train recedes from a stationary observer at 30.0m/s. What frequency does the observer hear? f’ = ] = 403 Hz

14. When the speed of an aircraft exceeds the speed of sound, the aircraft overtakes the wave fronts. The sound is confined to a conical region, the Mach cone In a time, t, the aircraft moves a distance VE t and the initial sound wave moves vt. The sharp pressure disturbance at the surface of the cone is heard as a loud bang = sonic boom

15. Diffraction • Deflection of waves at the edge of an obstacle • The amount of diffraction increases with the ratio of wavelength to the size of the gap fanlike beams spread out forming a diffraction pattern

16. Example: The minimum size of a structure that can be detected in an ultrasound image is limited by diffraction. With careful analysis of echoes reflected from structures within the body, features as small as one-quarter of a wavelength can be imaged. Suppose the probe uses ultrasound with a frequency of 2.0 x 106Hz. What is the smallest feature that can be detected? λ