Chapter 16 Waves and Sound

A wave is a traveling disturbance. 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 Longitudinal Wave

16.1 The Nature of Waves Transverse Wave

over again by the source. 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.

In the drawing, one cycle is shaded in color. 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.

Example 1 The Wavelengths of Radio Waves 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

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 file:///Users/silvinagatica/Desktop/class/simulations/applets/sim24.htm

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 Low E

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 phase: Φ (in radians) Interpretation of the formula: y=0 for Φ=0 This happens for: x represents the position of a point traveling with speed v, to the right After t=T, x moved to

16.4 The Mathematical Description of a Wave y=0 for Φ= 0 This happens for: This is the position of a point traveling with speed v, to the left

16.4 The Mathematical Description of a Wave Example: A wave is represented by the expression: y= 2cm Sin(3 s-1 t – 5 m-1 x) Find the amplitude of the wave. Find the frequency. Find the wavelength Find the speed What is the direction of propagation?

16.4 The Mathematical Description of a Wave We compare with the general expression Example: A wave is represented by the expression: y= 2cm Sin(3 s-1 t – 5 m-1 x) Find the amplitude of the wave. Find the frequency. Find the wavelength Find the speed What is the direction of propagation? A=2cm b) c) d) e) to the right

Check your understanding 16.1.2. Mike is holding one end of a Slinky. His hand moves up and down and causes a transverse wave to travel along the Slinky away from him. Is the motion of Mike’s hand a wave? a) Yes, the motion of Mike’s hand is a wave because it moves up and down in periodic motion. b) Yes, the motion of Mike’s hand is a wave because Mike is transferring energy to the Slinky. c) No, the motion of Mike’s hand is not a wave because there is no traveling disturbance. d) No, the motion of Mike’s hand is not a wave because there is no energy traveling along the Slinky.

16.2.2. The drawing shows the vertical position of points along a string versus distance as a wave travels along the string. Six points on the wave are labeled A, B, C, D, E, and F. Between which two points is the length of the segment equal to one wavelength? a) A to E b) B to D c) A to C d) A to F e) C to F

16. 2. 3. A longitudinal wave with an amplitude of 0 16.2.3. A longitudinal wave with an amplitude of 0.02 m moves horizontally along a Slinky with a speed of 2 m/s. Which one of the following statements concerning this wave is true? a) Each particle in the Slinky moves a distance of 2 m each second. b) Each particle in the Slinky moves a vertical distance of 0.04 m during each period of the wave. c) Each particle in the Slinky moves a horizontal distance of 0.04 m during each period of the wave. d) Each particle in the Slinky moves a vertical distance of 0.02 m during each period of the wave. e) Each particle in the Slinky has a wavelength of 0.04 m.

16. 3. 1. The tension of a guitar string in increased by a factor of 4 16.3.1. The tension of a guitar string in increased by a factor of 4. How does the speed of a wave on the string increase, if at all? a) The speed of a wave is reduced to one-fourth the value it had before the increase in tension. b) The speed of a wave is reduced to one-half the value it had before the increase in tension. c) The speed of a wave remains the same as before the increase in tension. d) The speed of a wave is increased to two times the value it had before the increase in tension. e) The speed of a wave is increased to four times the value it had before the increase in tension.

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.

Sound travels through gases, liquids, and solids at considerably 16.6 The Speed of Sound Sound travels through gases, liquids, and solids at considerably different speeds.

Conceptual Example 5 Lightning, Thunder, and a Rule of Thumb 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?

Sound waves carry energy that can be used to do work. 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.

Example 6 Sound Intensities 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

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 area of sphere

The decibel (dB) is a measurement unit used when comparing two sound 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: 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

Example 9 Comparing Sound Intensities 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

16.11 The Sensitivity of the Human Ear

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

Example 10 The Sound of a Passing Train 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

Numerator: plus sign applies when observer moves towards the 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