Chapter 16 Waves and Sound 16 1 The Nature of Waves 1 A wave is a traveling disturbance 2 A wave carries energy from place to place 16 1 The Nature of Waves Transverse Wave 16 1 The Nature of Waves Longitudinal Wave 16 1 The Nature of Waves Water waves are partially transverse and partially longitudinal 16 2 Periodic Waves Periodic waves consist of cycles or patterns that are produced over and over again by the source In the figures every segment of the slinky vibrates in simple harmonic motion provided the end of the slinky is moved in simple harmonic motion 16 2 Periodic Waves In the drawing one cycle is shaded in color The amplitude A is the maximum excursion of a particle of the medium from the particles undisturbed position The wavelength is the horizontal length of one cycle of the wave The period is the time required for one complete cycle The frequency is related to the period and has units of Hz or s 1 1 f T 16 2 Periodic Waves v f T 16 2 Periodic Waves Example 1 The Wavelengths of Radio Waves AM and FM radio waves are transverse waves consisting of electric and magnetic field disturbances traveling at a speed of 3 00x108m s A station broadcasts AM radio waves whose frequency is 1230x103Hz and an FM radio wave whose frequency is 91 9x106Hz Find the distance between adjacent crests in each wave v f T v f 16 2 Periodic Waves AM FM v 3 00 108 m s 244 m 3 f 1230 10 Hz v 3 00 108 m s 3 26 m 6 f 91 9 10 Hz 16 3 The Speed of a Wave on a String The speed at which the wave moves to the right depends on how quickly one particle of the string is accelerated upward in response to the net pulling force tension F v m L linear density 16 3 The Speed of a Wave on a String Example 2 Waves Traveling on Guitar Strings Transverse waves travel on each string of an electric guitar after the string is plucked The length of each string between its two fixed ends is 0 628 m and the mass is 0 208 g for the highest pitched E string and 3 32 g for the lowest pitched E string Each string is under a tension of 226 N Find the speeds of the waves on the two strings 16 3 The Speed of a Wave on a String High E v F 226 N 826 m s 3 m L 0 208 10 kg 0 628 m Low E F 226 N v 207 m s 3 m L 3 32 10 kg 0 628 m 16 3 The Speed of a Wave on a String Conceptual Example 3 Wave Speed Versus Particle Speed Is the speed of a transverse wave on a string the same as the speed at which a particle on the string moves 16 4 The Mathematical Description of a Wave What is the displacement y at time t of a particle located at x 16 5 The Nature of Sound Waves LONGITUDINAL SOUND WAVES 16 5 The Nature of Sound Waves The distance between adjacent condensations is equal to the wavelength of the sound wave 16 5 The Nature of Sound Waves Individual air molecules are not carried along with the wave 16 5 The Nature of Sound Waves THE FREQUENCY OF A SOUND WAVE The frequency is the number of cycles per second A sound with a single frequency is called a pure tone The brain interprets the frequency in terms of the subjective quality called pitch 16 5 The Nature of Sound Waves THE PRESSURE AMPLITUDE OF A SOUND WAVE Loudness is an attribute of a sound that depends primarily on the pressure amplitude of the wave 16 6 The Speed of Sound Sound travels through gases liquids and solids at considerably different speeds 16 6 The Speed of Sound In a gas it is only when molecules collide that the condensations and rerefactions of a sound wave can move from place to place vrms Ideal Gas kT v m 3kT m k 1 38 10 23 J K 5 7 or 3 5 16 6 The Speed of Sound Conceptual Example 5 Lightning Thunder and a Rule of Thumb There is a rule of thumb for estimating how far away a thunderstorm is After you see a flash of lighting count off the seconds until the thunder is heard Divide the number of seconds by five The result gives the approximate distance in miles to the thunderstorm Why does this rule work 16 6 The Speed of Sound LIQUIDS Bad v SOLID BARS Y v 16 7 Sound Intensity Sound waves carry energy that can be used to do work The amount of energy transported per second is called the power of the wave The sound intensity is defined as the power that passes perpendicularly through a surface divided by the area of that surface P I A 16 7 Sound Intensity Example 6 Sound Intensities 12x10 5W of sound power passed through the surfaces labeled 1 and 2 The areas of these surfaces are 4 0m2 and 12m2 Determine the sound intensity at each surface 16 7 Sound Intensity P 12 10 5 W 5 2 I1 3 0 10 W m A1 4 0m 2 P 12 10 5 W 5 2 I2 1 0 10 W m A2 12m 2 16 7 Sound Intensity For a 1000 Hz tone the smallest sound intensity that the human ear can detect is about 1x10 12W m2 This intensity is called the threshold of hearing On the other extreme continuous exposure to intensities greater than 1W m2 can be painful If the source emits sound uniformly in all directions the intensity depends on the distance from the source in a simple way 16 7 Sound Intensity power of sound source P I 4 r 2 area of sphere 16 7 Sound Intensity Conceptual Example 8 Reflected Sound and Sound Intensity Suppose the person singing in the shower produces a sound power P Sound reflects from the surrounding shower stall At a distance r in front of the person does the equation for the intensity of sound emitted uniformly in all directions underestimate overestimate or give the correct sound intensity P I 4 r 2 16 8 Decibels The decibel dB is a measurement unit used when comparing two sound intensities Because of the way in which the human hearing mechanism responds to intensity it is appropriate to use a logarithmic scale called the intensity level I 10 dB log Io I o 1 00 10 12 W m 2 Note that log 1 0 so when the intensity of the sound is equal to the threshold of hearing the intensity level is zero 16 8 Decibels I 10 dB log Io I o 1 00 10 12 W m 2 16 8 Decibels Example 9 Comparing Sound Intensities Audio system 1 produces a sound intensity level of 90 0 dB and system 2 …