Sound Chapter 17

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

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)

Intensity of Sound I Intensity is expressed on a logarithmic scale, (dB) decibel

Example Express the threshhold of hearing (2.5 x W/m 2 ) and the threshhold of pain (1.0 W/m 2 ) in decibels. Solution: (10dB)x log 10 (2.5x W/m 2 ) = (10dB) x log 10 (2.5) = 4.0 dB 1.0x W/m 2 (10dB)x log 10 (1.0 W/m 2 ) = (10dB) x log ) = 120 dB 1.0x W/m 2

(10dB)x log 10 (0.28 W/m 2 ) = (10dB) x log 10 (0.28 x ) = 114 dB 1.0x W/m 2 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 = r 1 2 I 1 = (30m) 2 I 1 = (2.8 x ) x I 1 = (2.8 x ) x (10 W/m 2 ) = 2.8 W/m 2 r 2 2 (180m) 2

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

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 λ 1 = 4L, λ 2 = 4/3L, λ 3 = 4/5L, λ 4 = 7/4L, … Eigenfrequencies: (f = v/ λ) f 1 = v/4L, f 2 = 3v/4L, f 3 = 5v/4L, …

A tube open at both ends: eigenfrequencies

The Doppler Shift 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. f’/ f = v’/v f’ = f (1 ± V R /v) Doppler shift, moving receiver

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 - V R /v) f’ = 440Hz (1 – 30 m/s/331 m/s)= 400Hz f’ = f (1 - V R /v) f’ = 0.62Hz (1 – 6.0m/s/2.5 m/s)= -0.87Hz

Doppler shift, moving emitter 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?

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 V E 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

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