Midterm Physics 113
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Lab Question
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1. d)

            Period = (0.1 ms/division)x(4 division) =.4 ms
            Frequency = 1/.0004 s= 2500 Hz

2. d) 

            At resonance we have a maximum applitude 

A1. a)      frequency must be constant since the
            wave peaks are conserved. 
            Wave peaks are not destroyed.
A2. b)
            d sin(th) = m lambda   tan(th)=y/L

          so for small angles

            d y/L = m lambda
            d = L m lambda/y = 10.*650nm/.002= 3.25 mm

A3. a)      tan(th)=n2/n1=1.33 ->  th=53 degrees

A4. c)      I=I0/2 cos(45)**4 = I0/8

A5. c)      2.5 lambda sin(th) = m lambda
            th = 90 degrees
            2.5 = m -> m=-2,-1,1,2 (for singles slit m=0 doesn't exist)

            4 dark fringes visible

A6. c)      m = gamma * m0 = 3 * m0   -> gamma =3
            KE = mo c^2 (gamma-1)= 2 m0 c^2
 
A7. e)      1.67x10^{-27}/sqrt(1-.866**2) = 3.34x10^{-27} kg

A8. d)         f=v/(2L) v=sqrt(T/(m/l)) -> f1/f2=sqrt(T1/T2)
             f2=f1*sqrt(T2/T1) = 300 *sqrt(2) = 424 Hz


B1. b)       sound is a longitudinal wave

B2. a)       only horizontal light reflected. To remove it polarization
             axis must be vertical
B3. a)       f=lamda/(4L)


B4. b)       rainbows caused by dispersion

B5. b)         one phase shift -> 2t=m lambda dark
               for m=0 we have t=0

C1.          
             on phase shift -> 2t=m lambda/n minimum
                               2t=(m+1/2)lambda/n maximum

             set m=0  t=lamba/(4 n) = 400/(4 1.33) = 75.2 nm

C2.

            displacement
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          distance(a-n) = 3.5 m/3 = 1.67 m

          f=3*v/(4L)=3*343/(4*3.5)=73.5 Hz

C3.
        First Postulate: Laws of physics apply in any inertial frame
        Second Postulate: Speed of light is c as observed from any inertial frame

C4.     d sin(th) = m lambda

        d = m lambda/sin(th) = 1 (650 nm)/sin(35) = 1133.2 nm

        N = 1/d = 1/(1133.2x10^{-9}m 100 cm/m) = 8832 lines/cm


C5.     convert rocket time to earth time
           
         20/sqrt(1-.866**2) = 40 years


         d = v *t  = 0.866 c * 40 years = 34.64 c-years
                                        or 2.22x10^{18} meters