Copyright © 2012 Pearson Education Inc. PowerPoint ® Lectures for University Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Chapter 15 Mechanical Waves Modifications by Mike Brotherton and Jim Verley
Copyright © 2012 Pearson Education Inc. Goals for Slightly Abbreviated Chapter 15 To study the properties and varieties of mechanical waves To relate the speed, frequency, and wavelength of periodic waves To interpret periodic waves mathematically To calculate the speed of a wave on a string To calculate the energy of mechanical waves To understand the interference of mechanical waves To analyze standing waves on a string
Copyright © 2012 Pearson Education Inc. Introduction Earthquake waves carry enormous power as they travel through the earth. Other types of mechanical waves, such as sound waves or the vibration of the strings of a piano, carry far less energy. Marvel’s Skye AKA Daisy Johnson AKA “Quake” has the power to amplify mechanical vibrations.
Copyright © 2012 Pearson Education Inc. Types of mechanical waves A mechanical wave is a disturbance traveling through a medium. Figure 15.1 below illustrates transverse waves and longitudinal waves.
Copyright © 2012 Pearson Education Inc. Periodic waves For a periodic wave, each particle of the medium undergoes periodic motion. The wavelength of a periodic wave is the length of one complete wave pattern. The speed of any periodic wave of frequency f is v = f.
Copyright © 2012 Pearson Education Inc. Periodic transverse waves For the transverse waves shown here in Figures 15.3 and 15.4, the particles move up and down, but the wave moves to the right.
Copyright © 2012 Pearson Education Inc. Periodic longitudinal waves For the longitudinal waves shown here in Figures 15.6 and 15.7, the particles oscillate back and forth along the same direction that the wave moves. Follow Example 15.1.
Copyright © 2012 Pearson Education Inc. Mathematical description of a wave The wave function, y(x,t), gives a mathematical description of a wave. In this function, y is the displacement of a particle at time t and position x. The wave function for a sinusoidal wave moving in the +x-direction is y(x,t) = Acos(kx – t), where k = 2π/ is called the wave number. Figure 15.8 at the right illustrates a sinusoidal wave.
Copyright © 2012 Pearson Education Inc. The speed of a wave on a string Follow the first method using Figure above. Follow the second method using Figure at the right. The result is
Copyright © 2012 Pearson Education Inc. Calculating wave speed Follow Example 15.3 and refer to Figure below.
Copyright © 2012 Pearson Education Inc. Power in a wave A wave transfers power along a string because it transfers energy. The average power is proportional to the square of the amplitude and to the square of the frequency. This result is true for all waves. Follow Example 15.4.
Copyright © 2012 Pearson Education Inc. Wave intensity The intensity of a wave is the average power it carries per unit area. If the waves spread out uniformly in all directions and no energy is absorbed, the intensity I at any distance r from a wave source is inversely proportional to r 2 : I 1/r 2. (See Figure at the right.) Follow Example 15.5.
Copyright © 2012 Pearson Education Inc. Wave interference and superposition Interference is the result of overlapping waves. Principle of super- position: When two or more waves overlap, the total displacement is the sum of the displace- ments of the individual waves. Study Figures and at the right.
Copyright © 2012 Pearson Education Inc. Standing waves on a string Waves traveling in opposite directions on a taut string interfere with each other. The result is a standing wave pattern that does not move on the string. Destructive interference occurs where the wave displacements cancel, and constructive interference occurs where the displacements add. At the nodes no motion occurs, and at the antinodes the amplitude of the motion is greatest. Figure on the next slide shows photographs of several standing wave patterns.
Copyright © 2012 Pearson Education Inc. Photos of standing waves on a string Some time exposures of standing waves on a stretched string.
Copyright © 2012 Pearson Education Inc. PowerPoint ® Lectures for University Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman Lectures by Wayne Anderson Chapter 16 Sound and Hearing Modifications by Mike Brotherton and Jim Verley
Copyright © 2012 Pearson Education Inc. Goals for Abbreviated Chapter 16 To describe sound waves in terms of particle displacements or pressure variations To calculate the speed of sound in different materials To calculate sound intensity To find what determines the frequencies of sound from a pipe To learn why motion affects pitch
Copyright © 2012 Pearson Education Inc. Introduction Most people prefer listening to music instead of noise. (Is that statement a no-brainer?) We can think of a sound wave either in terms of the displace- ment of the particles or of the pressure it exerts. How do humans actually perceive sound? Why is the frequency of sound from a moving source different from that of a stationary source? Beware Black Canary’s sonic scream!
Copyright © 2012 Pearson Education Inc. Sound waves Sound is simply any longitudinal wave in a medium. The audible range of frequency for humans is between about 20 Hz and 20,000 Hz. Ultrasonic sound waves have frequencies above human hearing and infrasonic waves are below. Figure 16.1 at the right shows sinusoidal longitudinal wave.
Copyright © 2012 Pearson Education Inc. Different ways to describe a sound wave Sound can be described by a graph of displace-ment versus position, or by a drawing showing the displacements of individual particles, or by a graph of the pressure fluctuation versus position. The pressure amplitude is p max = BkA. B is the bulk modulus from Ch. 11, which we skipped, where B=-p(x,t)/(dv/V)
Copyright © 2012 Pearson Education Inc. Speed of sound waves The speed of sound depends on the characteristics of the medium. Table 16.1 gives some examples. The speed of sound:
Copyright © 2012 Pearson Education Inc. The speed of sound in water and air Follow Example 16.3 for the speed of sound in water, using Figure 16.8 below. Follow Example 16.4 for the speed of sound in air.
Copyright © 2012 Pearson Education Inc. Sound intensity The intensity of a sinusoidal sound wave is proportional to the square of the amplitude, the square of the frequency, and the square of the pressure amplitude. Study Problem-Solving Strategy Follow Examples 16.5, 16.6, and 16.7.
Copyright © 2012 Pearson Education Inc. The decibel scale The sound intensity level is = (10 dB) log(I/I 0 ). Table 16.2 shows examples for some common sounds.
Copyright © 2012 Pearson Education Inc. Examples using decibels Follow Example 16.8, which deals with hearing loss due to loud sounds. Follow Example 16.9, using Figure below, which investigates how sound intensity level depends on distance.
Copyright © 2012 Pearson Education Inc. Standing sound waves and normal modes The bottom figure shows displacement nodes and antinodes. A pressure node is always a displace- ment antinode, and a pressure antinode is always a displacement node, as shown in the figure at the right.
Copyright © 2012 Pearson Education Inc. The Doppler effect The Doppler effect for sound is the shift in frequency when there is motion of the source of sound, the listener, or both. Use Figure below to follow the derivation of the frequency the listener receives.
Copyright © 2012 Pearson Education Inc. The Doppler effect and wavelengths Study Problem-Solving Strategy Follow Example using Figure below to see how the wavelength of the sound is affected.
Copyright © 2012 Pearson Education Inc. The Doppler effect and frequencies Follow Example using Figure below to see how the frequency of the sound is affected.
Copyright © 2012 Pearson Education Inc. A moving listener Follow Example using Figure below to see how the motion of the listener affects the frequency of the sound.