You Dont Know, What You Dont Know A Journey toward Food Security.
Dont Believe Everything the Professor Tells You
1
January/February — Vol. 28, No. 1 3 E D I T O R I A L By Robert Fleming Don’t Believe Everything the Professor Tells You! Recently I reviewed a manuscript on space charge detection in insulators, and the subject of acoustic impedance arose in the context of the transmission of acoustic waves through the samples. This remind- ed me of a surprising discussion on acous- tic impedance and the transmission of sound waves through gases, which I read many years ago in an excellent little book called “Thinking like a physicist—Phys- ics problems for undergraduates,” edited by Norman Thompson from the Univer- sity of Bristol (Adam Hilger, Bristol, IOP Publishing Ltd., 1987). Many of you have likely seen, perhaps in your first year at university, a demon- stration that purports to show that sound waves cannot propagate in a vacuum. The equipment probably consisted of an evacuable glass bell jar containing an electric bell. The bell was clearly audible throughout the lecture theatre. The pro- fessor started the vacuum pump, probably the rotary vane type, and the sound of the bell rapidly decreased until it became al- most inaudible. He or she then claimed to have shown that sound waves cannot propagate in a vacuum, explaining that a better pump would have eliminated the sound of the bell completely. It is un- doubtedly true that sound waves cannot propagate in vacuum. Alas, this “demon- stration” is spurious! The minimum pressure attainable in a bell jar sealed with an O-ring, using a rotary vane pump, would be of order 10 –2 cm Hg, or about 13 Pa if you insist on SI units. At this pressure and at room tem- perature, the mean free path of air mol- ecules is approximately 7 × 10 −4 m (see any elementary physics text). If the bell frequency is of order 300 Hz, the cor- responding wavelength is around 1.1 m. Because the mean free path of the air molecules is much smaller than the wave- length of the sound waves, the waves will propagate perfectly well through the air in the bell jar! So why does the sound intensity drop as the air pressure falls? The reason is that the acoustic impedance mismatch between the air and the glass of the bell jar increases as the pressure falls, and so the amount of energy reflected from the glass increases. The acoustic impedance Z of a material is (ρE) 0.5 , where ρ is its density and E is the appropriate elastic modulus. The fraction of the energy of a plane wave, incident on a planar glass surface from air, that will be reflected is (Z air − Z glass ) 2 /(Z air + Z glass ) 2 . Z air is linearly proportional to the pressure; even though it is much less than Z glass at atmospheric pressure, it falls further as the bell jar is evacuated, and it is this further reduction that causes the sound to disappear. The sound waves “bounce” off the glass, and very little energy is transmitted to the lec- ture theatre. This analysis contains many approxi- mations. The glass surface and the sound waves are not planar, and re-entry of the sound waves into the air and internal re- flections within the glass should be taken into account. However, there can be little doubt that the thrust of the analysis is cor- rect. If your appetite for a physics chal- lenge has been whetted by the above, try this, the last problem in the book. It takes about four minutes to boil a 60-g hen egg, to be acceptable to most people for eating. For how long would it be advisable to boil an ostrich egg weighing 1.5 kg? Hint: Assume that the eggs have the same chemical composition, the same shape, and the same thermal properties. No more data are required. The boiling time is not linearly proportional to the mass of the egg.
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Transcript of Dont Believe Everything the Professor Tells You
January/February — Vol. 28, No. 1 3
E D I T O R I A L
By Robert Fleming
Don’t Believe Everything the Professor Tells You!
Recently I reviewed a manuscript on space charge detection in insulators, and the subject of acoustic impedance arose in the context of the transmission of acoustic waves through the samples. This remind-ed me of a surprising discussion on acous-tic impedance and the transmission of sound waves through gases, which I read many years ago in an excellent little book called “Thinking like a physicist—Phys-ics problems for undergraduates,” edited by Norman Thompson from the Univer-sity of Bristol (Adam Hilger, Bristol, IOP Publishing Ltd., 1987).
Many of you have likely seen, perhaps in your first year at university, a demon-stration that purports to show that sound waves cannot propagate in a vacuum. The equipment probably consisted of an evacuable glass bell jar containing an electric bell. The bell was clearly audible throughout the lecture theatre. The pro-fessor started the vacuum pump, probably the rotary vane type, and the sound of the bell rapidly decreased until it became al-most inaudible. He or she then claimed to have shown that sound waves cannot propagate in a vacuum, explaining that a better pump would have eliminated the sound of the bell completely. It is un-doubtedly true that sound waves cannot propagate in vacuum. Alas, this “demon-stration” is spurious!
The minimum pressure attainable in a bell jar sealed with an O-ring, using a rotary vane pump, would be of order 10–2
cm Hg, or about 13 Pa if you insist on SI units. At this pressure and at room tem-perature, the mean free path of air mol-ecules is approximately 7 × 10−4 m (see any elementary physics text). If the bell frequency is of order 300 Hz, the cor-responding wavelength is around 1.1 m. Because the mean free path of the air molecules is much smaller than the wave-length of the sound waves, the waves will propagate perfectly well through the air in the bell jar!
So why does the sound intensity drop as the air pressure falls? The reason is that the acoustic impedance mismatch between the air and the glass of the bell jar increases as the pressure falls, and so
the amount of energy reflected from the glass increases. The acoustic impedance Z of a material is (ρE)0.5, where ρ is its density and E is the appropriate elastic modulus. The fraction of the energy of a plane wave, incident on a planar glass surface from air, that will be reflected is (Z
air − Z
glass)2/(Z
air + Z
glass)2. Z
air is linearly
proportional to the pressure; even though it is much less than Z
glass at atmospheric
pressure, it falls further as the bell jar is evacuated, and it is this further reduction that causes the sound to disappear. The sound waves “bounce” off the glass, and very little energy is transmitted to the lec-ture theatre.
This analysis contains many approxi-mations. The glass surface and the sound waves are not planar, and re-entry of the sound waves into the air and internal re-flections within the glass should be taken into account. However, there can be little doubt that the thrust of the analysis is cor-rect.
If your appetite for a physics chal-lenge has been whetted by the above, try this, the last problem in the book. It takes about four minutes to boil a 60-g hen egg, to be acceptable to most people for eating. For how long would it be advisable to boil an ostrich egg weighing 1.5 kg?
Hint: Assume that the eggs have the same chemical composition, the same shape, and the same thermal properties. No more data are required. The boiling time is not linearly proportional to the mass of the egg.
