最佳解答40分:為何每升1個攝氏度,音速會增加?

2007-01-16 2:06 am
下面資料輯自《維基百科》:
音波可以在固體、液體或是氣體介質中傳播,介質密度愈大,則音速愈快。在空氣中,音速又會依空氣之狀態(如濕度、溫度、密度)不同而有不同數值。如攝氏零度之海平面音速約為 331.5m/s(1193 km/h);一萬米高空之音速約為 295m/s(1062 km/h);另外每升高1攝氏度,音速就增加0.607m/s。
根據上述資料,每高一個攝氏度,空氣密度理應減少,音速也應該遞減,但為何上文卻指出音速會增加0.607m/s?
更新1:

感謝Guttvennnnn作出詳盡的解說,但我仍有一問: E(楊氏模數)是什麼? 我是文科的學生,對熱學的認知只限於中三程度而已,煩請告知~

更新2:

那在E這個數據不變的情況下,為何「介質密度愈大,則音速愈快」? 還是藍色螢光筆的是M變得比p大時才成立; 而綠色螢光筆的是m不變才成立?

更新3:

「介質密度愈大,則音速愈快」 介質密度愈大(代入空氣為介質,情況就是溫度下降了) 溫度變化前後M不變(因為是同一個物質嘛?) 根據藍色螢光字,溫度(介質)下降了(密度變大),音速不是愈快嗎? 為何提高溫度又會音速增加? **抱歉 我的物理觸覺實在太差 難為你了"

更新4:

本來密度愈小,音速愈大我是明白的,唯藍色部分的陳述令我費解。

回答 (5)

2009-06-02 10:03 am
hard to understand
2007-01-18 4:54 pm
聲音在固體中傳送,用楊氏模數(Young's modulus)解釋無可厚非,在流體(即液體、氣體)中可以解釋嗎?
聲音在空氣中傳送,A0、ΔL、L0又是甚麼?空氣可以量度stress、strain和有fracture嗎?
空氣的楊氏模數又可以得出嗎?空氣的楊氏模數可以解釋升溫的影響嗎?
2007-01-16 2:15 am
Air pressure and temperature are what actually affect the speed of sound. As your altitude increases, air pressure and temperature decrease, and so does the speed of sound. When air particles are warmer, they move and carry sound waves faster, but when they are cold, they travel slowly, carrying sound waves slowly.

vsolids > vliquids > vgases
The speed of a sound wave in air depends upon the properties of the air, namely the temperature and the pressure. The pressure of air (like any gas) will effect the mass density of the air (an inertial property) and the temperature will effect the strength of the particle interactions (an elastic property). At normal atmospheric pressure, the temperature dependence of the speed of a sound wave through air is approximated by the following equation:

v = 331 m/s + (0.6 m/s/C)*T
where T is the temperature of the air in degrees Celsius. Using this equation is used to determine the speed of a sound wave in air at a temperature of 20 degrees Celsius yields the following solution.

v = 331 m/s + (0.6 m/s/C)*T
v = 331 m/s + (0.6 m/s/C)*20 C

v = 331 m/s + 12 m/s

v = 343 m/s

(The above equation relating the speed of a sound wave in air to the temperature provides reasonably good speed values for temperatures between 0 and 100 Celsius. The equation itself does not have any theoretical basis; it is simply the result of inspecting temperature-speed data for this temperature range. Other equations do exist which are based upon theoretical reasoning and provide accurate data for all temperatures. Nonetheless, the equation above will be sufficient for our use as introductory Physics students.)

At normal atmospheric pressure and a temperature of 20 degrees Celsius, a sound wave will travel at approximately 343 m/s; this is approximately equal to 750 miles/hour. While this speed may seem fast by human standards (the fastest humans can sprint at approximately 11 m/s and highway speeds are approximately 30 m/s), the speed of a sound wave is slow in comparison to the speed of a light wave. Light travels through air at a speed of approximately 300 000 000 m/s; this is nearly 900 000 times the speed of sound. For this reason, humans can observe a detectable time delay between the thunder and lightning during a storm. The arrival of the light wave from the location of the lightning strike occurs in so little time that it is essentially negligible. Yet the arrival of the sound wave from the location of the lightning strike occurs much later. The time delay between the arrival of the light wave (lightning) and the arrival of the sound wave (thunder) allows a person to approximate his/her distance from the storm location. For instance if the thunder is heard 3 seconds after the lightning is seen, then sound (whose speed is approximated as 345 m/s) has traveled a distance of

distance = v * t = 345 m/s * 3 s = 1035 m
If this value is converted to miles (divide by 1600 m/1 mi), then the storm is a distance of 0.65 miles away.
2007-01-16 2:15 am
Increase temperature not means density will increase. Increase temperature will increase the kinetic energy of each gas particule, so the speed of sound will increase.
The statement of green part may be give the volume be constant, so the density will not be change at this occasion.
2007-01-16 2:12 am
音障是一種物理現象,當物體(通常是航空器)的速度接近音速時,將會逐漸追上自己發出的聲波。聲波疊合累積的結果,會造成震波(Shock Wave)的產生,進而對飛行器的加速產生障礙,而這種因為音速造成提升速度的障礙稱為音障。

突破音障進入超音速後,從航空器最前端起會產生一股圓錐形的音錐,在旁觀者聽來這股震波有如爆炸一般,故稱為音爆或聲爆(Sonic Boom)。強烈的音爆不僅會對地面建築物產生損害,對於飛行器本身伸出衝擊面之外部分也會產生破壞。

除此之外,由於在物體的速度快要接近音速時,周邊的空氣受到聲波疊合而呈現非常高壓的狀態,因此一旦物體穿越音障後,周圍壓力將會陡降。在比較潮濕的天氣,有時陡降的壓力所造成的瞬間低溫可能會讓氣溫低於它的露點(Dew Point)溫度,使得水氣凝結變成微小的水珠,肉眼看來就像是雲霧般的狀態。但由於這個低壓帶會隨著空氣離機身的距離增加而恢復到常壓,因此整體看來形狀像是一個以物體為中心軸、向四周均勻擴散的圓錐狀雲團。


音速也是聲速,即聲音在介質中傳播之速度。音波可以在固體、液體或是氣體介質中傳播,介質密度愈大,則音速愈快。在空氣中,音速又會依空氣之狀態(如濕度、溫度、密度)不同而有不同數值。如攝氏零度之海平面音速約為 331.5m/s(1193 km/h);一萬米高空之音速約為 295m/s(1062 km/h);另外每升高1攝氏度,音速就增加0.607m/s。


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