Chapter 15.1 Notes
Chapter 15: Sound
Sound, is a longitudinal mechanical wave produced as one molecule bumps into another molecule. The velocity of a sound wave depends on the temperature of the air; the speed in air is 331.5 m/s at 0º C. This speed increases with temperature about 0.6 m/s)/Cº .
The speed of sound is directly proportion to the elasticity of the vibrating medium, and it is inversely proportion to the inertia of the medium. In general, denser media tend to support faster sound velocities. Some examples you should be familiar with
- Air: 343 m/s at 20°C
- Salt Water: approx. 1500 m/s (less for fresh water)
- Steel: 5150 m/s
- As a wave source advances in the direction of the waves it is producing, waves tend to crowd together. Imagine a locomotive that is blowing its whistle at a constant frequency. Study this diagram. As soon as the "crest" of one wave moves forward, away from the train, the train moves so as to catch up with that crest before it creates a new one. This causes the waves to be artificially closer together than they would be if the train was not moving. While the engineer inside the train, moving at the same speed as the train, hears the whistle at its normal frequency.. an observer toward whom the train is approaching would perceive a higher frequency.
- The opposite effect occurs as a wave source moves away from an observer. The train above would move away from the crest of one wave before it emits a new one, and the waves become artificially farther apart, creating a lower perceived frequency by this observer.
- The same thing will happen if a light source is moving. Look at this diagram. If the light bulb is approaching an observer, the observer perceives a shorter (bluer) wavelength. This is called blue shift. If the light source moves away from the observer, the observer perceives a red shift. We can thus tell that celestial bodies like stars are moving away from us if the light we see from them is more toward the red end of the spectrum.
- NOTE: The same effects are manifest if the source is stationary, and the observer is moving. All that matters is that there is relative velocity between the source and the observer.
- What do you think... if you are approaching a red light at an intersection, if you speed up, could you "blue shift" the light to green, and legally pass through the intersection?
The perceived frequency due to doppler shift can be calculated as follows:
- is the perceived frequency,
- f is the frequency emitted by the source,
- v is the velocity of the wave through the medium under the current conditions,
- vd is the velocity of the detector relative to the source. If the detector is moving toward the source, this value is POSITIVE. If it is moving away, it is NEGATIVE
- vs is the velocity of the source relative to the detector. If the source is moving toward the detector, this value is POSITIVE. If it is moving away, it is NEGATIVE
Practice: solve problems 11 and 12 in the chapter review problems, and problems 9 and 10 in the supplementary set on page 699 of the text.
Here are a couple of links where you do an interactive internet activity with the Doppler effect:
Pitch and Loudness
Frequency and intensity are physical characteristics of sound.
- Intensity is defined as the power of the sound over the area through which sound energy flows or I =P/A. Sound itself is a mental perception of a soundwave that strikes our tympanic membrane. There can be sound intensity even if there is no one there to hear the sound!
- The term "pitch" is our interpretation of sound's frequency. Humans can hear sounds that are within the range of approximately 20 Hz through 18,000 Hz. Most humans can't really hear above 16,000 Hz.
- The term loudness is our interpretation of a sound's intensity.
- Sound level is a little different than sound intensity, but is still related to the perceived loudness of a sound. Sound level is measured in units called decibels (dB) and is a ratio of the pressure (N/m2) of the sound to the pressure caused by the most faintly audible sound.
- Humans can detect sounds if they create as little as 2.0 x 10-5 N/m2 on the eardrum. Sounds of this amplitude are at a zero decibel level.
- Sounds that create a pressure amplitude of 10 times this value (2.0 x 10-4 N/m2) have a level of 20 dB.
- Ten times this pressure again ( 2.0 x 10-3 N/m2 ) produces a level of 40 dB.
- Ten times that value ( 2.0 x 10-2 N/m2 ) produces a 60 dB level.
- Jet aircraft can produce sounds at 120 dB. 120/20 = 6 so this is 106 times louder than the least audible sound!
Resonance occurs when a vibration is reinforced at the natural frequency of some object, and the frequency is amplified. A sound vibration passing through a tube may cause air in the tube to vibrate at the same frequency as the sound wave, and thus the sound becomes louder. This only happens if the tube itself is of a particular length relative to the wavelength of the sound:
- tubes that are closed on one end will resonate a sound if the tube is at 1/4 the wavelength of the frequency, or any 1/2 wavelength increment above that.
- tubes that are open on both ends will resonate a sound if the tube is 1/2 the wavelength of the frequency, or any 1/2 wavelength increment above that.
homework: set #1 ch 15 probs 1-6. set #2 problems 24-33. set #3 problems 7-12, 34-38
video: The Tacoma Narrows Bridge
lab: experimentally determine the frequency of tuning forks using resonance.