Chapter 12 Lecture Chapter 12: Mechanical Waves and Sound
Goals for Chapter 12 To describe mechanical waves. To study superposition, standing waves and sound. To present sound as a standing longitudinal wave. To see that waves will interfere (add constructively and destructively). To study sound intensity and beats. To solve for frequency shifts (the Doppler effect). To examine applications of acoustics and musical tones.
Mechanical Waves Figure 12.1 Waves in a fluid are the result of a mechanical disturbance. At right, a stone disturbs water and creates visually observable traveling waves.
Types of Mechanical Waves Figure 12.2 Transverse the wave disturbance is perpendicular to the direction of propagation. Longitudinal the wave disturbance is parallel to the direction of propagation. Water waves a complex mixture of both.
Generating a Longitudinal Wave Figure 12.3 An object undergoing SHM can cause the disturbance and the medium can be a string, cord, or rope under tension.
"Time Lapse" Snapshot of a Traveling Wave Figure 12.4 If you follow the original set of markers (3 red dots at top of the figure), you can see the movement as time passes going down from top to bottom. Each fresh sketch as you go downward elapses 1/8 of the period. Recall that 8/8T (all the way from top to bottom) is one period, the time for one complete oscillation to pass.
λf = v wave Example 12.1 We know that for any wave, the wavelength (in meters) times the frequency (in 1/s or Hz) will multiply to give the velocity of the wave (in m/s). Sound in air, sound in water, sound in metal, light this relationship will guide us. Refer to the worked example for sound in air at 20 o C.
Longitudinal and Transverse Waves Figures 12.5 and 12.6 help us to see the sinusoidal waveform.
Waves on a Long Rope Under Tension Example 12.2 Refer to Figure 12.7. The velocity of the wave will depend on the type and size of rope as well as the tension we add with our geological sample. Follow the example on pages 358 and 359.
We Can Solve Equation 12.5 As Needed Figure 12.9 Follow the explanation on pages 360 and 361. We can express the wave in terms of trigonometric functions and observable data.
Waves Can Reflect Figure 12.11
Waves Can Superimpose Figure 12.12 Two waves come in from opposite directions. Each wave has amplitude inverted with respect to the other. During the superposition, there is nearly cancellation. After the collision, the outgoing waves resemble those that came in, with the sign of the amplitude inverted. The details are a complex function of time.
Waves Become Coherent (Standing) Figure 12.14 When nodes and antinodes align, there is no destructive interference and a steady-state condition is established. Depending on the shape and size of the medium transmitting the wave, different standing wave patterns are established as a function of energy.
Normal Modes for a Linear Resonator Figure 12.16 The resonator is fixed at both ends. Wave energy increases as you go down the y- axis below.
Fundamental Frequencies Figure 12.17 The fundamental frequency depends on the properties of the resonant medium. If the resonator is a string, cord, or wire, the standing wave pattern is a function of tension, linear mass density, and length.
Standing Waves on a String Example 12.3 Refer to the worked example at the bottom of page 367. The bass viol follows the same logic as Quantitative Analysis 12.4.
Longitudinal Standing Waves Figure 12.20 Kundt's tube. A resonator closed at both ends must trap a wave with nodes at both ends (analogous to the transverse waves on a string).
Speed of Sound in Hydrogen Example Speed of Sound in Hydrogen Example Refer to Example 12.4 on page 369.
A New Resonator, the Organ Pipe Figure 12.23 With a chamber closed at one end, the With a chamber closed at one end, the resonant waves must have nodes at the
A Resonator Open at Both Ends Figure A 12.25 Resonator Open at Both Ends Figure other such instruments in the orchestra. Since the resonant chamber is open at both ends, the waves therein must have antinodes at both ends. Refer to the worked
Human Hearing Figure 12.29 Refer to pages 373 377. 20 20,0000 Hz is the approximate range of human hearing. Refer to Below pages that 373 377. is infrasonic and above. 20 20,0000 Note, there are Hz slight is the variations approximate between range animal of human species hearing. Below that is infrasonic and above.
Sound Intensity and the Decibel Scale Figure 12.30 Use Table 12.2 to see logarithmic db examples of common sounds. Use Table 12.2 to see logarithmic db examples of common sounds.
Beats and the Beat Frequency Figure 12.31 Two slightly different tuning forks will ring more loudly at the difference of the frequencies.
The Doppler Effect Figure 12.32 Shifts in observed frequency can be caused by motion of the source, the listener, or both. Refer to Examples 12.10 12.13.