Chapter 13

 6)    T = 1/f -- where f is the frequency
       f = 1/T = 1/0.025 = 40 Hz

 8)    initial period of oscillation      T_initial = 1/f_1 
       final period of oscillation        T_final   = 1/f_2
       where f_1 and f_2 are initial and final frequencies. 
        T_final - T_initial = 1/f_1 - 1/f_2 = 1/0.5 - 1/0.25 = -2 sec
       --->  Period of oscillation will decrease by 2 seconds.    
        
13)    a) T = 1/f, where f is the frequency
          ---> T = 1/10^12 Hz = 10^(-12)s
       b) for the angular velocity omega and amplitude of oscillation A
          the velocity is v = A*omega and omega = 2*pi*f 
            v = 10^(-11)m * 2*pi*10^(12)Hz = 62.8 m/s

18)    Total energy of the spring is constant
           E_total = E_kinetic + E_potential
       At a point of equilibrium the potential energy is zero and the kinetic
       energy is at a maximum
           E_kinetic = m * v^2 / 2
       At that point  
         E_total = E_kinetic = m * v^2 / 2 = 
                 = 0.2kg * 0.95^2 m^2/sec^2 / 2 = 0.09 J

30)    For mass m=0.25kg and spring constant k=200N/m, 
       the period of oscillations is T = 2*pi*sqrt(m/k)
          T = 2 * 3.14 * sqrt(0.25 kg/200 N/m) = 0.22 s
       The frequency is f = 1/T = 4.5 Hz

58)    The light wavelength lambda is given by the speed of light c and
       its frequency f
               lambda = c / f
       lambda = 3*10^8 m/sec / 4.3 * 10^14 Hz = 7.0 * 10^(-7) m

59)    Again the relation between the wavelenght, frequency and speed is
               lambda = v / f
       lambda_min = v / f_max = 345 m/sec / 20000 Hz = 0.017 m
       lambda_max = v / f_min = 345 m/sec / 20 Hz    = 17 m
       
62)    The distance between first and second crests is 0.75 m
       The distance between first and third crest is 2*0.75 =  1.5 m
       The distance between first and 13th crest is  12*0.75 = 9.0 m
       The speed of the wave = distance/time
            v =  9.0 m / 3 s =  3 m/s