Chapter 15: Sounds Properties of Sound: 1. Propagates in a longitudinal wave. 2. Alternating series of high pressure (compression) and low pressure (rarefaction).

Compressions and rarefactions

3. Speed defined by the wavelength and frequency of a wave 3. Speed defined by the wavelength and frequency of a wave. v = wavelength x frequency a. wavelength: distance between compressions. b. frequency (Hz): the number of oscillations in time.

Velocity Characteristics of the velocity of sound: 1. depends on temperature and medium a. vacuum: no sound b. cool air moves slower than warm air due to refraction (bends more in cool air) ie: ‘Red October’ c. normal 343 m/s @ 20oC and 1 atm or 331 m/s + (0.6 m/s ) T = 343 m/s d. exhibits properties of reflection, refraction, interference, and diffraction

e. has areas of cancellation (nodes. called the ‘dead-spot’ e. has areas of cancellation (nodes called the ‘dead-spot’. Area where the waves cancel.

f. Speed of sound depends on the the elasticity of the medium. g f. Speed of sound depends on the the elasticity of the medium. g. Sound travels 4x faster in liquids and 15x faster in solids as compared to air. h. Properties that affect the speed of sound in air are (1) pressure, (2) denisity of the medium and (3) the molecular mass of the medium.

Sampler A sound wave has a frequency of 261.6 Hz at 20oC. What is the wavelength? ans: 1.31 m 2. Sound with a frequency of 261.6 Hz travels through water at a speed of 1435 m/s. Find the wavelength in water? ans: 5.485 m 3. Find the frequency of a sound wave at 20oC with a wavelength of 0.667 m? ans: 514 Hz HW: #1-5, p 405 and #31 & 33, p424

The Doppler Shift The apparent shift in frequency as a sound source approaches a listener. Note a decrease wavelength is an increase in frequency.

The Doppler Shift Equation: fd = fs [ v + vd / v – vs ] fd = frequency detected fs = frequency from the source v = standard velocity of sound in air @ 20oC vd = Speed of the detector (person hearing the sound) vs = speed from the source

Doppler Shift A train whistles sounds at a frequency of 500 Hz as it approaches the terminal traveling at 40 m/s. A person at the terminal at rest would detect a frequency of what?

Relationship Pitch and Frequency Pitch and frequency are the same Octave: frequency changes in a 2:1 ratio For every doubling of frequency, the octave change by 1 2(f) = 1 ovtave higher ½(f) = 1 octave lower C @ 262 Hz = C @ 523 or 523/2 = 262 F @ 349.2 Hz = 698.4 Hz or 698.4/2 = 349.2

Loudness The amplitude of the wave defines the loudness of the sound. Loudness is measured in decibels (dB). This unit is derived from the ratio of the pressure of the sound to the pressure of the lightest sound

Resonance Sound is produced by the vibration of matter. If the vibration of the sound is equal to the natural vibration of the material, then the wave vibration is additive. Results in a standing wave

Closed-end Resonator Tube with one end closed. Vibrations travel down the column and then reflect back. When the vibrations are in phase, ‘resonance’ occurs at a region of high pressure(gets louder) . L = λ/4 L = v / 2f λ = 4L L = 3λ/4 λ = 4L/3 L = 5λ/4 λ = 4L/5 Resonance Spacing = λ/2 L = v / 2f from a v = λf equation

Open-ended Resonance Both end at open: In phase vibrations occur at a region of lower pressure. First Harmonic: L = λ / 2 λ = 2L Second Harmonic: L = ʎ λ = L Third Harmonics: L = 3λ/2 λ = 2L/3

Open and Closed Ended Resonator

Sampler 1. An automatic focus camera is able to focus on objects by use of an ultrasonic sound wave. The camera sends out sound waves which reflect off distant objects and return to the camera. A sensor detects the time it takes for the waves to return and then determines the distance an object is from the camera. If a sound wave (speed = 340 m/s) returns to the camera 0.150 seconds after leaving the camera, how far away is the object? Ans: 25.5 m

What is the frequency in Hertz of the sound wave? 2. The annoying sound from a mosquito is produced when it beats its wings at the average rate of 600 wingbeats per second. What is the frequency in Hertz of the sound wave? Ans: 600 Hz Assuming the sound wave moves with a velocity of 340 m/s, what is the wavelength of the wave? Ans: 0.567 m

3. Doubling the frequency of a wave source doubles the speed of the waves. True or False? Ans: False, 2x frequency = ½ wavelength Speed is uneffected by frequency 4. Playing middle C on the piano keyboard produces a sound with a frequency of 256 Hz. Assuming the speed of sound in air is 345 m/s, determine the wavelength of the sound corresponding to the note of middle C. Ans: 1.35 m

5. An elephant produces a 10 Hz sound wave 5. An elephant produces a 10 Hz sound wave. Assuming the speed of sound in air is 345 m/s, determine the wavelength of this infrasonic sound wave. Ans: 34.50m 6. Determine the speed of sound on a cold winter day in Glenview (T=3 C). Ans: 332.8 m/s

7. Two sound waves are traveling through a container of nitrogen gas 7. Two sound waves are traveling through a container of nitrogen gas. Wave A has a wavelength of 1.5 m. Wave B has a wavelength of 4.5 m. The velocity of wave B must be __________ the velocity of wave A. a. one-ninth b. one-third c. the same as d. three times larger than Ans: c , the medium did not change

8. Two sound waves are traveling through a container of nitrogen gas 8. Two sound waves are traveling through a container of nitrogen gas. Wave A has a wavelength of 1.5 m. Wave B has a wavelength of 4.5 m. The frequency of wave B must be __________ the frequency of wave A. a. one-ninth b. one-third c. the same as d. three times larger than Ans: b, increase λ, decrease f