Chapter 14: Sound

1. Chapter 14: Sound Suggested homework problems: 11,26,33,44,50 • Sound waves • Sound waves are longitudinal waves traveling through a medium, • such as air. Producing a Sound Wave

2. Producing a Sound Wave • Movement of air molecules in a sound wave • When a tine swings to the right, the molecules in an element of air • in front of its movement are forced closer together than normal: • compression • When the tine swings to the left the molecules in an element of air • to the right of the tine spread apart, and the density and air pressure • in this region are then lower than normal: rarefaction rarefaction compression

3. Characteristics of Sound Waves • Longitudinal wave vs. transverse wave • The motion of the elements of the medium in a longitudinal sound • wave is back and forth along the direction in which the wave travels. • In a transverse wave, the vibrations of the elements of the medium • are at right angle to the direction of travel of the waves. • Categories of sound waves • Audible waves : Frequencies in the range of sensitivity of the • human ears – 20 to 20,000 Hz • Infrasonic waves : Frequencies below the audible range • Ultrasonic waves : Frequencies above the audible range

4. Characteristics of Sound Waves • Application of ultrasound • Ultrasonic sound waves have frequencies greater than 20 kHz and, • as the speed of sound is constant for given temperature and medium, • they have shorter wavelength. Shorter wavelengths allow them to • image smaller objects and ultrasonic waves are, therefore, used as • a diagnostic tool and in certain treatments. • Imaging organs of a body • Internal organs can be examined • via the images produced by the • reflection and absorption of • ultrasonic waves. Use of ultrasonic • waves is safer than x-rays but • images show less details. • Certain organs such as the liver • and the spleen are invisible to • x-rays but visible to ultrasonic waves. • Measurement of blood flow using the Doppler effect

5. Characteristics of Sound Waves • Application of ultrasound (cont’d) • Mechanism to produce ultrasonic waves (piezoelectric effect) : An alternating voltage of high frequency induces vibration on a crystal of quartz and strontium titanate etc. of the same frequency. This vibration of the crystal creates a beam of ultrasonic waves. This process can be reversed, so the transmitter can also work as the receiver. • Principle of ultrasonic imaging: A sound wave is partially reflected whenever it is incident on a boundary between two materials having different densities. The percentage of the incident wave intensity reflected (PR) when a sound wave is traveling in a material of density ri and strikes a material of density rt is given by:

6. Characteristics of Sound Waves • Application of ultrasound (cont’d) • Use of ultrasound for imaging Physicians commonly use ultrasonic waves to observe fetuses. This technique presents far less risk than do x-rays, which deposit more energy in cells and can produce birth defects. • Cavitron ultrasonic surgical aspirator (CUSA) This device is used to surgically remove brain tumors. The probe of the CUSA emits ultrasonic waves (~23 kHz) at its tips. When the tip touches a tumor, the part of the tumor near the probe is shattered and the residue can be sucked up through the hollow probe. • A device to break up kidney stones • Instantaneous measurement of the distance to an object Instantaneous measurement of an object to be photographed by a camera can be done using ultrasonic waves.

7. Speed of Sound • Speed of sound wave in a fluid • The speed of a sound wave in a fluid depends on the fluid’s • compressibility and inertia. B : bulk modulus of the fluid r : equilibrium density of the fluid • Speed of sound wave in a solid rod Y : Young’s modulus of the rod r : density of the fluid • Speed of sound wave in air 343 m/s at T=20oC

8. Energy and Intensity of Sound waves • Average intensity of a wave • The average intensity of a wave on a given surface is defined as • the rate at which energy flows through the surface, DE/Dt, divided • by the surface area A: SI unit : watt per meter squared (W/m2) • A rate of energy transfer is power : P : the sound power passing through the surface • Thresholds The faintest sounds the human ear can detect at a frequency of 1 kHz have an intensity of about 1x10-12 W/m2 – Threshold of hearing The loudest sounds the human ear can tolerate have an intensity of about 1 W/m2 – Threshold of pain

9. Energy and Intensity of Sound waves • Intensity level in decibel • The loudest tolerable sounds have intensities about 1.0x1012 times • greater than the faintest detectable sounds. • The sensation of loudness is approximately logarithmic in the human • ear. Because of that the relative intensity of a sound is called the • intensity level or decibel level, defined by: I0 = 1.0x10-12 W/m2 : the reference intensity the sound intensity at the threshold of hearing Threshold of hearing Threshold of pain

10. Energy and Intensity of Sound waves • Intensity level in decibel • Intensity levels in decibels for different sources • Example 14.2: A noisy grinding machine A noisy grinding machine in a factory produces a sound intensity of 1.00x10-5 W/m2. (a) Calculate the intensity level of the single grinder. (b) If a second machine is added, then: (c) Find the intensity corresponding to an intensity level of 77.0 dB.

11. Spherical and Plane Waves • Intensity of a spherical wave • If a small spherical object oscillates so that its radius changes • periodically with time, a spherical sound wave is produced. • The energy in a spherical wave pro- • pagates equally in all directions. • At a distance r the intensity of a • spherical sound wave form the • source is: rays wave fronts

12. Spherical and Plane Waves • Wave fronts, rays, and plane waves • A series of circular arcs at maximum intensity concentric with the • source of spherical waves are called wave fronts. The distance • between the adjacent wave fronts equals the wavelength l. • The radial lines pointing outward from the source and perpendicular • to the arcs are called rays. • If the distance from the source is much greater than the wavelength, • we can approximate the wave fronts with parallel planes called • plane waves.

13. Spherical and Plane Waves • Example 14.3: Intensity variations of a point source • A small source emits sound waves with a power output of 80.0 W. • (a) Find the intensity 3.00 m from the source. (b) At what distance would the intensity be one-fourth as much as it is at r=3.00 m? (c) Find the distance at which the sound level is 40.0 dB?

14. Doppler Effect • Doppler effect of sound wave • Frequency of the sound wave heard by an observer depends • on the motion of the sound source and the observer: Doppler effect. • This phenomenon is common to all waves including light. • Case 1 : The observer moving to a stationary source Source at rest Listener moving left Source at rest Listener moving right

15. Doppler Effect • Case 1 : The observer moving to a stationary source fS : frequency of the source lS : wavelength of the source v : speed of sound in air fO : frequency heard by the observer relative speed of the sound w.r.t. the observer The observer is moving away from the source

16. Doppler Effect • Case 2 : The source is moving to a stationary observer When the source moves

17. Doppler Effect • Case 2 : The source is moving to (away from) a stationary observer The wavelength lO observed by the observer O is shorter (longer) than the wavelength lS of the source at rest. The source moves by vsT =vs/fs in one period • for moving to • +for moving away

18. Doppler Effect • General case When the observer moves toward the source, a positive speed is substituted for vO. When the observer moves away from the source, a negative speed is substituted for vO. When the source moves toward the observer, a positive speed is substituted for vS. When the source moves away from the source, a negative speed is substituted for vS.

19. Doppler Effect • Example 14.5 : The noisy siren. An ambulance travels down a highway at a speed of 75.0 mi/h, its siren emitting sound at a frequency of 4.00x102 Hz. What frequency is heard by a passenger in a car traveling at 55.0 mi/h in the opposite direction as the car and ambulance: (a) approach each other and (b) pass and move away from each others? First convert the speeds from mi/h to m/s. (a) (b)

20. Interference of Sound Waves • Two sound waves interfere each other Imagine two sound waves from two separate sound point sources. destructive constructive d2 d1 two waves enhance each other two waves destruct each other

21. Interference of Sound Waves • Example 14.6 : Two speakers driven by the same source Two speakers placed 3.00 m apart are driven by the same oscillator. A listener is originally at Point O, which is located 8.00 m from the center of the line connecting the two speakers. The listener then walks to point P, which is a perpendicular distance 0.350 m from O, before reaching the first minimum in sound intensity. What is the frequency of the oscillator? Take speed of sound in air to be 343 m/s.

22. Standing Waves • Superposition of two waves moving in the same direction • Superposition of two waves moving in the opposite direction

23. Standing Waves • Reflection of waves at a fixed end Reflected wave is inverted

24. Standing Waves • Standing waves on a string Superposition of two waves moving in the opposite direction creates a standing wave when two waves have the same speed and wavelength. N=node, AN=antinode

25. Standing Waves • Standing waves on a string There are infinite numbers of modes of standing waves first overtone second overtone fundamental frequency third overtone L fixed end fixed end

26. Standing Waves Superposition of two waves moving in the opposite direction creates a standing wave when two waves have the same speed and wavelength. N=node, AN=antinode

27. Standing Waves • Standing waves in air column Sound wave in a pipe with two open ends

28. Standing Waves • Standing waves in air column Sound wave in a pipe with two open ends

29. Standing Waves • Standing waves in air column Normal modes in a pipe with two open ends 2nd normal mode

30. Standing Waves • Standing waves in air column Sound wave in a pipe with one closed and one open end (stopped pipe)

31. Standing Waves • Standing waves in air column Normal modes in a pipe with an open and a closed end (stopped pipe)

32. Two interfering sound waves can make beat Two waves with different frequency create a beat because of interference between them. The beat frequency is the difference of the two frequencies. Beats

33. Resonance • When we apply a periodically varying force to a system that can • oscillate, the system is forced to oscillate with a frequency equal • to the frequency of the applied force (driving frequency): forced • oscillation. When the applied frequency is close to a characteristic • frequency of the system, a phenomenon called resonance occurs. Resonance • Resonance also occurs when a • periodically varying force is applied • to a system with normal modes. • When the frequency of the applied • force is close to one of normal • modes of the system, resonance • occurs. works as a stoppeded pipe

34. Example 14.10 The sound waves generated by the fork are reinforced when the length of the air column corresponds to one of the resonant frequencies of the tube. Suppose the smallest value of L for which a peak occurs in the sound intensity is 9.00 cm. • Find the frequency of the • tuning fork. Resonance Lsmallest=9.00 cm (b) Find the wavelength and the next two water levels giving resonance.

35. Resonance Resonance

36. Timbre or tone color or tone quality Frequency spectrum noise music Quality of Sound Harmonics piano piano Harmonics