文档介绍：Spring Term 2003
Intro. APPLIED NUCLEAR PHYSICS
Problem Set #1
1. Wave Interference:
Give a general expression for the amplitude at point, P , as a function of, θ,interms
of the amplitude, A, of the ing wave, the distance between the slits, d,and the
wavelength, λ.
λ P
r2
r1
d θ
Figure 1: Wave Interference Diagram
1
2. The equation of a transverse wave traveling along a string is given by,
y =[π( 50t)]
−
where, y, and, x, are in centimeters and, t, is in seconds.
Find the amplitude, wavelength, wave number, frequency, period, and velocity of
• the wave.
Find the maximum transverse speed of any particle along the string.
•
3. Liboff,,,,,
2
Problem Set 1 Solution
1. Wave Interference
Solution
S2
b
S1
D
Assume S1 and S2 are two identical sources. Their electric ponents at point P can be
expressed as:
E1 (t) = E cosωt (1)
E2 (t) = E cos(ω+t φ) (2)
φ
Ep
E2
E1
Use phasor representation, the resulting interference wave electric ponent is:
2 2 2 2
E p = E + E − 2E cos(π−φ)
2 2 2 2
E p = 2E + 2E cosφ= 2E (1 + cosφ)
φ
E 2 = 4E 2 cos 2 (3)
p 2
The phase difference φ is associated with path difference as:
φ r − r
= 2 1
2πλ
d sinθ
If D >> d , r − r ≈ d sinθ⇒φ≈ 2π(4)
2 1 λ
Problem Set 1 Solution
E 2
Also we know the intensity of the wave is I =
2m0C
2
E p
Thus I p =
2µ0C
2
E 2 φ 2 φ
Insert (3), we get I p = × 4cos = 4I 0 cos (5)
2µ0C 2 2
φ d sinθ
In summary, I = 4I cos 2 , φ≈ 2π
p 0 2 λ
2. Solution
(a) Transverse Wave: displacement of medium is perpendicular to the direction of travel of the
wave. The displacement of a particle on the string at location x and time t can be expressed
as: y(x, t) = Asin 2π(t / T + x / λ) (1)
2π
Among them, A: amplitude, T: period, λ: wavelength, k = : wave number,
λ
1 λ
f = : frequency, v = : velocity.
T T