CHAPTER 13 - SOUND

13.1 – SOUND WAVES Objectives * Explain how sound waves are produced * Relate frequency to pitch * Compare the speed of sound in various media * Relate plane waves to spherical waves * Recognize the Doppler effect, and determine the direction of a frequency shift when there is relative motion between a source and an observer.

WHERE SOUND WAVES COME FROM Sound starts with a vibrating object When an object vibrates, it sets the air molecules near it in motion As a vibrating object moves to the right, the molecules on the right forced closer together. This becomes a region of higher molecular density and pressure. This is an area of compression. As the vibrating object moves to the left, the molecules in the region to the right now spread father apart, causing lower molecular density and pressure. This is an area of rarefaction.

SOUND WAVES ARE LONGITUDINAL Longitudinal Waves and Particle Motion What is the definition of a longitudinal wave? A wave in which the direction of the vibrating particles are parallel to the direction of wave travel

FREQUENCY AND PITCH Review: What is frequency? Frequency is the number of cycles (or vibrations or oscillations, etc.) per unit time. The units for cycles per second, or Hertz (Hz). Audible sound waves for the average human are between 20 and 20,000 Hz. Infrasonic sound waves are those with frequencies below 20 Hz Ultrasonic sound waves are those with frequencies above 20,000 Hz

FREQUENCY AND PITCH, CONT. Pitch is how high or low we perceive a sound wave to be. The higher the frequency of a sound wave, the higher pitch we perceive it to be. Frequency is an objective, measureable quantity, while pitch is simply a perception….

SOUND WAVES AND IMAGES Sound waves with very short wavelengths (i.e., ultrasonic waves) can be used to create visible images. Sound waves are partially reflected when they reach a boundary between materials of two different densities. Ultrasonic waves, with their very short wavelengths, are easily reflected off small objects.

SOUND WAVES AND IMAGES Another example of using sound waves to form images is called echolocation (or sonar). Dolphins and bats can send out high frequency sound wave pulses that are reflected back. The reflected waves allow the dolphin or bat or to form an image of the object that caused the wave reflection.

SPEED OF SOUND The speed of sound depends on the medium it is traveling through. Sound can travel through solids, liquids or gases. Because sounds waves travel via particle vibration, the speed of sound depends on how fast a medium can transfer its motion from one particle to another. So, which medium would you expect sound to travel through faster….a solid or a gas?

SPEED OF SOUND, CONT. The speed of sound also is dependent on the temperature of the medium, especially for gases. As air gets warmer, the air molecules move around more and collide more frequently. Therefore, sound vibrations moving from particle to particle can happen faster in warmer air. For liquids and solids, temperature does not make much of a difference because the molecules are so close together anyway. V = (T) v is in m/s and T is in o C

HOW SOUND WAVES TRAVEL We’ve seen pictures and animations of longitudinal waves, and they all appear to be one-dimensional. But sound waves propagate in 3 dimensions. The areas of compression are called wavefronts. The distance between consecutive wavefronts is a wavelength. The direction of wave travel is spherically outward (shown by red arrows).

THE DOPPLER EFFECT The pitch of the car horn gets higher as the car gets closer to us, and gets lower as the car gets farther away…. But pitch is related to frequency, and the frequency of the car horn isn’t changing, so how does this work?

THE DOPPLER EFFECT, CONT. Remember, pitch is the “perception” of frequency. The relative motion of the car makes this perception change. As the car approaches you, the wavefronts from the horn reach you more frequently because the source of the sound is moving toward you. As the source of the sound moves away from you, you perceive the pitch to be lower because the wavefronts don’t reach you as frequently.

DOPPLER EFFECT EQUATION f o = frequency the observer hears v o = velocity of observer v s = velocity of source f s = normal frequency of the source sound (in air) v = normal speed of sound in air (343 m/s)

USING THE DOPPLER EQUATION If the OBSERVER is stationary: Then v o = 0 f o decreases as source goes away from observer. For f o to decrease, the denominator on the right side has to increase. To increase denominator, use (v + v s ). f o increases as source gets closer to observer. For f o to increase, the denominator on the right side has to decrease. To decrease denominator, use (v - v s ).

USING THE DOPPLER EQUATION, CONT. If the SOURCE is stationary: Then v s = 0 f o decreases as observer goes away from the source. For f o to decrease, the numerator on the right side has to decrease. To decrease numerator, use (v - v o ). f o increases as observer gets closer to the source. For f o to increase, the numerator on the right side has to increase. To increase numerator, use (v + v o ).

DOPPLER EFFECT EXAMPLE PROBLEM A train with horn blaring passes a station going 50 m/s. If the people standing on the platform at the station hear the frequency as 384 Hz after the train passes, what is the frequency of the train horn? Ans: 440 Hz

13.2 – SOUND INTENSITY AND RESONANCE Objectives * Calculate the intensity of sound waves * Relate intensity, decibel level, and perceived loudness * Explain why resonance occurs

SOUND INTENSITY Intensity is the rate of energy flow through a unit area perpendicular to the direction of wave motion. Because power, P, is defined as the rate of energy transfer, we can also describe intensity in terms of power.

SOUND INTENSITY, CONT. Units for power are? Units for area are? So, units for intensity are? Since sound propagates outward in all directions equally, the area affected by the intensity is the surface area of a sphere (4  r 2 ). Where r is the distance from the sound source

SOUND INTENSITY, CONT. So, the farther you get away from the source of a sound, the less intense the sound because the energy of the sound is spread out over a larger area.

SOUND INTENSITY, EXAMPLE What is the intensity of sound waves produced by a trumpet at a distance of 3.2m if the power output of the trumpet is 0.20W? Assume the sound waves are spherical. Ans: 1.6 x W/m 2

INTENSITY AND FREQUENCY

RELATIVE INTENSITY – DECIBEL LEVEL Decibel level – is the relative intensity of a sound, determined by relating the intensity of a sound wave to the intensity at the threshold of hearing. Units are decibels (dB)

INTENSITY, DECIBELS AND LOUDNESS For each 10 dB increase in the decibel level of a sound, a sound will be approximately twice as loud. For each 10 dB increase in the decibel level of a sound, The intensity level of the sound is multiplied by 10.

INTENSITY, DECIBELS AND LOUDNESS EXAMPLE When the decibel level of traffic noise goes from 40 dB to 60 dB, how much louder does the traffic seem? How much greater is the sound intensity? Ans: 4 times as loud, intensity increases by a factor of 100

RESONANCE If the driving pendulum is set in motion, all the other pendulums will be “forced” into motion as well. But only one of them will oscillate at the same frequency as the driving pendulum. This is the pendulum with the same “natural frequency” as the driving pendulum.

RESONANCE, CONT. When the “forced vibration” matches the pendulum’s natural frequency, then the amplitude of the frequency will be much larger, and the system is in resonance.

RESONANCE AND SELF-DESTRUCTION

QUICK REVIEW – 13.1 AND 13.2 Pitch versus frequency – musical notes Velocity of sound in air based on air temperature Intensity / decibel / pain chart Doppler effect example calculation Intensity/decibel example calculation

MUSICAL NOTES PITCH AND FREQUENCY

TEMPERATURE EFFECT VELOCITY OF SOUND IN AIR v = ( T) You’ll need this formula for CH13 lab !!!!! What is the velocity of sound in air at 21 o C (70 o F) What is the velocity of sound in air at 38 o C (100 o F) m/s m/s

DOPPLER EFFECT EXAMPLE An ambulance races toward the scene of an accident at 35 m/s with its siren blaring at a frequency of 2000Hz. People in their cars pull over and stop as the ambulance approaches. At what frequency do they hear the siren as the ambulance approaches them? At what frequency do they hear it after it passes? (Assume v = 343 m/s) f o as approaching: 2227 Hz f o after passing: 1815 Hz

INTENSITY / DECIBEL / LOUDNESS You’re sitting in the front row of a Smashin’ Pumpkins concert, decibel level 110dB. When you get home, your mom makes you listen to the music at a much lower level, 70dB. How much less intense is the music at home than at the concert? How much quieter does the music seem to you at home? 4 steps of 10dB, each a factor of 10, so 10 4 or10,000 times less intense 4 steps of 10dB, each half as loud, (½*½*½*½) or 1/16 th as loud

13.3 HARMONICS Standing waves 1 st harmonic (f 1 ) = “fundamental frequency” 2 nd harmonic (f 2 ) = 2 * f 1 3 rd harmonic (f 3 ) = 3 * f 1 nth harmonic (f n ) = n * f 1

HARMONICS, CONT. For any fixed length (L), each harmonic represents ½ wavelength So for the 4 th harmonic: L = 4 (½ ) L = 2 = ½ L Harmonics and Wavelength

HARMONICS, CONT. Standing waves on a vibrating string: f n = frequency of the nth harmonic n = harmonic number v = velocity of the wave on the string L = length of the vibrating string

WAVES ON A STRING, EXAMPLE A string on a toy guitar is 34.5cm long. a)What is the wavelength of its first harmonic? b)When the string is plucked, the speed of waves on the string is 410 m/s. What are the frequencies of the first three harmonics?

STANDING WAVES IN AN AIR COLUMN

For pipes OPEN at both ends: f n = (nv) / 2L f n = frequency of the nth harmonic n = harmonic number v = velocity of sound in the pipe L = length of the vibrating air column

STANDING WAVES IN AN AIR COLUMN For pipes CLOSED at one end: f n = (nv) / 4L f n = frequency of the nth harmonic n = harmonic number v = velocity of sound in the pipe L = length of the vibrating air column

OPEN PIPE EXAMPLE What are the first three harmonics in a 2.45m long open pipe? Assume that the speed of sound trough the pipe is 345 m/s.

Standing waves on a string Standing waves in an open pipe

Standing waves in a pipe closed at one end

LAB INSTRUCTIONS DO NOT TAP/BANG THE TUNING FORKS ON ANYTHING HARD!!! You must share the tuning forks Clean up your lab station when finished! Ok to leave the cylinder, tube, tuning forks and mallet at the lab table HAND IN YOUR LAB REPORT BEFORE YOU LEAVE!!!