Chapter 16 Waves and Sound You may not realize it, but you are surrounded by waves. The “waviness” of a water wave is readily apparent, from the ripples on a pond to ocean waves large enough to surf. It’s less apparent that sound and light are also waves. Chapter Goal: To learn thebasic properties of traveling waves.
16.1 The Nature of Waves • A wave is a traveling disturbance. • A wave carries energy from place to place.
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 cycleis shaded in color. The amplitude A is the maximum excursion of a particle of the medium from the particles undisturbed position. SI units are meters. The wavelength λis the horizontal length of one cycle of the wave. SI units are meters. The period T is the time required for one complete cycle. SI units are seconds.
16.2 Periodic Waves In the drawing, one cycleis shaded in color. The frequency f is the number or waves (or cycles) that pass by in a given time. The units are cycles per second, called the Hertz (Hz), or s-1. Frequency is the reciprocal of period. the speed of a wave through some medium is:
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 (note that this is the speed of light !) 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. AM stands for “amplitude modulated” FM stands for “frequency modulated” Both of these methods allow sound to be carried over long distances.
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.
16.2 Periodic Waves AM FM AM radio signals are broadcast using a lower frequency than FM: therefore the waves have a much longer wavelength than FM. Back in the day, on a long road trip through the endless fields of Kansas and Nebraska, you’d have to switch to AM to get radio reception, and you know that meant country western…..or even worse, talk radio!
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 linear density
The speed of a wave pulse QUESTION:
EXAMPLE 20.1 The speed of a wave pulse m/L m/L m/L m/L
Ratio problem The graphs below show amplitude as a function of position (that means position is on the x-axis and frequency is not shown). Assume string 1 and 2 have the same length. The mass of string 1 is twice the mass of string and the string tension in string 1 is 8x the tension in string 2. A wave of the same amplitude and frequency travels on each of the strings. Using the relationship v = sqrt (F/m/L), and the relationship v = f λ, determine which of the pictures correctly shows the waves.
Ratio problem The graphs below show amplitude as a function of position (that means position is on the x-axis and frequency is not shown). Assume string 1 and 2 have the same length. The mass of string 1 is twice the mass of string and the string tension in string 1 is 8x the tension in string 2. A wave of the same amplitude and frequency travels on each of the strings. Using the relationship v = sqrt (F/m/L), we find that v1 = 2v2 and if the frequency is equal in both cases, then λ1 = 2λ2 and A is correct.
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 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 rarefactions of a sound wave can move from place to place. These collisions are modeled as an adiabatic process For an ideal gas, the speed of sound is” k = Boltzmann’s constant T is the temperature in Kelvin (Tc + 273) γ (gamma) is the ratio of specific heat capacities at constant pressure to that of constant volume Cp/Cv γ = 5/3 for an ideal monatomic gas γ = 7/5 for an ideal diatomic gas “Air” is modeled as an ideal diatomic gas m is the mass of a molecule of the gas in kg
Speed of sound Carbon monoxide (CO), Hydrogen gas (H2) and nitrogen (N2) are all diatomic gases that behave as ideal. In which gas does sound travel the slowest at a given temperature? A. CO B. H2 C. N2
Speed of sound Carbon monoxide (CO), Hydrogen gas (H2) and nitrogen (N2) are all diatomic gases that behave as ideal. In which gas does sound travel the fastest at a given temperature? A. CO B. H2 C. N2 Answer: B, since hydrogen gas has the smallest mass
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 to area ratio. It is related (but not the same as!)to the loudness of the sound. • Recall the power is the energy per second released by the source • The energy released by the source, and therefore the power, are the same, regardless of the distance of the listener. • The intensity is proportional to the inverse square of the distance
If the source emits sound uniformly in all directions, the intensity depends on the distance from the source in a simple way. power of sound source area of sphere
Was it as good for you? Assume that the sound spreads out uniformly and any ground reflections can be ignored. Listener 2 is twice as far from the explosion as Listener 1. If L1 hears with an intensity of 1 W/m2, with what intensity does L 2 hear? a. 2 b. ½ c. 4 d. ¼ (units of W/m2)
Fireworks I2/I1 = (P/4πr22) = r1/r2. I2 is ¼ of I1 (P/4πr12)
Decibels – a measure of loudness • Human hearing spans an extremely wide range of intensities • threshold of hearing at ≈ 1 × 10−12 W/m2 • threshold of pain at ≈ 10 W/m2. • To cover the range, we use a logarithmic scale. Sorry about that. • It is logical to place the zero of this scale at the threshold of hearing. • We define the sound intensity level, expressed in decibels (dB), as: where I0 = 1 × 10−12 W/m2.
16.8 Decibels Example 9 Comparing Sound Intensities Audio system 1 produces a sound intensity level of 90.0 dB, and system 2 produces an intensity level of 93.0 dB. Determine the ratio of intensities.
16.8 Decibels β1 = 93 dB, β2 = 90 dB, Find I2/I1 Divide both sides by 10 dB Take the antilog of both sides Although I2 is twice that of I1, it is not twice as loud. Experimental data show that it takes a 10 dB difference for a sound to be perceived as “twice as loud”.
16.9 The Doppler Effect The Doppler effect is the change in frequency or pitch of the sound detected by an observer because the sound source and the observer have different velocities with respect to the medium of sound propagation.
16.9 The Doppler Effect MOVING SOURCE
16.9 The Doppler Effect source moving toward a stationary observer source moving away from a stationary observer
16.9 The Doppler Effect Example 10 The Sound of a Passing Train A high-speed train is traveling at a speed of 44.7 m/s when the engineer sounds the 415-Hz warning horn. The speed of sound is 343 m/s. What are the frequency and wavelength of the sound, as perceived by a person standing at the crossing, when the train is (a) approaching and (b) leaving the crossing?
16.9 The Doppler Effect approaching leaving
16.9 The Doppler Effect MOVING OBSERVER
16.9 The Doppler Effect Observer moving towards stationary source Observer moving away from stationary source
16.9 The Doppler Effect GENERAL CASE Numerator: plus sign applies when observer moves towards the source Denominator: minus sign applies when source moves towards the observer
16.10 Applications of Sound in Medicine By scanning ultrasonic waves across the body and detecting the echoes from various locations, it is possible to obtain an image.
16.10 Applications of Sound in Medicine Ultrasonic sound waves cause the tip of the probe to vibrate at 23 kHz and shatter sections of the tumor that it touches.
16.10 Applications of Sound in Medicine When the sound is reflected from the red blood cells, its frequency is changed in a kind of Doppler effect because the cells are moving.