Chapter 12 Sound

If a tree falls in the middle of a forest does it make a sound?

*Sound travels as a longitudinal wave. Sound is created by some variation of the pressure at the source of the sound. The regions of air where the molecules are close together (high pressure) are compressions. The regions of air where the molecules are far apart (low pressure) are rarefactions.

The speed of the molecules in the air affect the speed at which the compression of the wave is transmitted to neighboring molecules. The speed of molecules is related to the temperature of the air. Thus the speed of sound has the following approximate calculation:

v = 331 + 0.6 T m/s . (In this chapter T is measured in Celsius temperature units.)

What is the speed of sound at room temperature (20^o Celsius)?

Video Sprott Disk 2 Side 1 frame 440

What are the definitions of pitch?

audible

The loudness of a sound is measured in decibels. β (dB) = 10 log₁₀ (I / I_o )

I is the intensity of the wave, measured in Watts/m²

I_o is 1 X 10 ^–12 Watts/m²

Why do physicists use a logarithmic calculation for sound intensity?

SKIP Sections 12.3 and 12.4

review: *The principle of superposition: If two waves occupy the same space at the same time then the net displacement of the medium is the sum of the individual wave displacements. (This assumes that the medium does not exceed its elastic limit.)

If both waves have the same sign of displacement then the net displacement will be larger than each individual displacement. *This situation is called constructive interference. The two waves are said to be in phase. If the displacements have opposite signs then the net displacement will be smaller than the magnitude of the largest displacement. *This situation is called destructive interference. The two waves are said to be out of phase.

If two interfering waves have the same wavelengths and amplitudes and opposite directions of travel a standing wave is produced. There will be locations (nodes) at which the displacement of the medium is always zero. The distance between adjacent nodes is ½ wavelength. Between the nodes are antinodes. The medium has its maximum vibration at the antinodes. There is ¼ wavelength between a node and antinode.

*The lowest frequency of a standing wave is called the fundamental frequency. For a string anchored at both ends the fundamental frequency is

f₁ = V / (2L)

The harmonic frequencies are integer multiples of the fundamental frequency. f_n = n * f₁

The first harmonic is the fundamental frequency. The first overtone is the second harmonic.

What are the allowed frequencies on a string that is 70 cm long and has a mass of 5 grams?

Standing waves can be formed in air columns that are open at one end or both ends. If the column is open at both ends the frequencies are identical to the case of the string that is anchored at both ends.

Define: open tube closed tube

What are the possible harmonics for each type of tube?

Skip 12.6

Beats are produced when two waves which do not have the same frequency occupy the same space at the same time. The beat frequency is equal to the difference in the frequencies of the two waves.

*The change in frequency of sound due to relative motion of the source and receiver is called the Doppler effect. This effect occurs if the motion is such that the source is directly approaching or directly receding from the receiver. The situations that can occur are

1) observer and source are stationary or both the observer and the source are moving in the same direction at the same speed … no Doppler effect occurs

A Doppler effect (shift in frequency) occurs for all of the following

2) observer moves towards a stationary source

3) source moves towards a stationary observer

4) observer moves away from a stationary source

5) source moves away from a stationary observer

6) observer and source are both moving toward the other

7) observer and source are both moving away from the other

8) observer and source are both moving in the same direction but at different speeds

Video 2C Chapters 27 & 28

The relationship between the frequency detected by the observer, f’ , and the frequency generated by the source, f , is:

1. For the case of a moving source and 2. Moving observer

stationary observer and stationary source

12.9 Shock Waves and the Sonic Boom

We will discuss this if class time allows. It will not be covered on the exam.

12.10 Ultrasound and Medical Imaging

We will discuss this if class time allows. It will not be covered on the exam.

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