1 / 30

Mechanical Waves: Properties, Speed, and Interference

Learn about the properties and varieties of mechanical waves, and how to calculate their speed and energy. Understand wave interference and analyze standing waves on a string.

matthewbowen
Download Presentation

Mechanical Waves: Properties, Speed, and Interference

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 15 Mechanical Waves Modifications by Mike Brotherton and Jim Verley

  2. 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

  3. 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.

  4. Types of mechanical waves • A mechanical wave is a disturbance traveling through a medium. • Figure 15.1 below illustrates transverse waves and longitudinal waves.

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. The speed of a wave on a string • Follow the first method using Figure 15.11 above. • Follow the second method using Figure 15.13 at the right. • The result is

  10. Calculating wave speed • Follow Example 15.3 and refer to Figure 15.14 below.

  11. 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.

  12. 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 r2: I 1/r2. (See Figure 15.17 at the right.) • Follow Example 15.5.

  13. 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 15.20 and 15.21 at the right.

  14. 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 15.23 on the next slide shows photographs of several standing wave patterns.

  15. Photos of standing waves on a string • Some time exposures of standing waves on a stretched string.

  16. Chapter 16 Sound and Hearing Modifications by Mike Brotherton and Jim Verley

  17. 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

  18. 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!

  19. 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.

  20. 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 pmax = BkA. • B is the bulk modulus from Ch. 11, which we skipped, where B=-p(x,t)/(dv/V)

  21. 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:

  22. 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.

  23. 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 16.1. • Follow Examples 16.5, 16.6, and 16.7.

  24. The decibel scale • The sound intensity level  is  = (10 dB) log(I/I0). • Table 16.2 shows examples for some common sounds.

  25. Examples using decibels • Follow Example 16.8, which deals with hearing loss due to loud sounds. • Follow Example 16.9, using Figure 16.11 below, which investigates how sound intensity level depends on distance.

  26. 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.

  27. 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 16.27 below to follow the derivation of the frequency the listener receives.

  28. The Doppler effect and wavelengths • Study Problem-Solving Strategy 16.2. • Follow Example 16.14 using Figure 16.29 below to see how the wavelength of the sound is affected.

  29. The Doppler effect and frequencies • Follow Example 16.15 using Figure 16.30 below to see how the frequency of the sound is affected.

  30. A moving listener • Follow Example 16.16 using Figure 16.31 below to see how the motion of the listener affects the frequency of the sound.

More Related