課程名稱︰普通物理學甲
課程性質︰系定必修
課程教師︰梁啟德
開課學院：
開課系所︰材料系
考試日期（年月日）︰2009年1月12日
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是 感恩
（如未明確表示，則不予發放）
試題 :
1.Please prove that for an adiabatic (絕熱) expansion (膨脹) of an ideal gas,
the pressure p and the volume V obey pV^γ = a constant, where γ = Cp/Cv is the
ratio of the molar specific heats (莫耳比熱) for the gas. Cp is the molar
specific heat for a constant pressure process and Cv is the molar specific
heat for a constant volume process, respectively.(10%)
2.Two point sources S1 and S2, which are in phase and separated by a distance
D = 1.5λ, emit identical sound waves of wavelength λ as shown in Fig. 1.
What is the phase difference of the waves from S1 and S2 at point P1, which
lies on the perpendicular bisector of the distance D from the sources. (a)What
type of interference occurs at P1?(5%) (b)What are the phase difference and
type of interference at point P2?(5%)
│
│
S1
│_____________________________ P1
│
S2
│
│
│
│
P2
3.Determine the amplitude of the resultant wave when two sinusoidal string
waves having the same frequency and travelling in the same direction are
combined, if their amplitudes are 6.0 cm and 8.0 cm and they have phase
constants of 0 and π/2 rad, respectively(10%).(Hint:use Phasors)
∞
4.Please calculate ∫ e^(-x^2)x^4 dx (10%).
0
∞
5.Please prove(證明) that ∫ e^(-x^2)x^5 dx = 1 (10%).
0
6.A toy rocket moves at a speed of 242 m/s directly toward a stationary pole
while emitting sound waves at frequency f = 1250 Hz (a)What frequency f' is
sensed by a detector that is attached to the pole?(10%) (b)Some of the sound
reaching the pole reflects back to the rocket, which has an onboard detector.
What frequency f" does it detect?(10%) [Hint: The speed of sound is 343 m/s.
Please consider the Doppler effect 都卜勒效應].
7.Use the wave equation to find the speed of a wave given by
y(x,t) = (2.00mm)[(20 m^-1)x-(4.0s^-1)t]^0.5 (10%)
8.Please find the general solution(通解) of the following equation:
d^2y/dx^2 - 3 dy/dx + 2y = 0 . (10%)
9.Imagine a Carnot engine that operates between the temperatures TH = 850 K
and TL = 300 K. What is the efficiency of this engine? (10%)
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