Wave Motion

 

1.      The speed of light waves in air is 3.0 x 108 m/sec.  The speed of sound waves in air is 333 m/s.  How long between is the time between when the lightning flash is seen and the thunderclap is heard if the lightning flash is 1.0 km away?   

 

2.      A wave has a frequency of 1000 hz and a wavelength of 20 meters.  What is the velocity of the wave ? 

 

3.      The wavelength of light visible to the human eye is on the order of 5 x 10–7 m.  If the speed of light in air is 3 x 108 m/s, find the frequency of the light wave. 

 

4.      The speed of a sound wave in seawater is approximately 1500 m/s.  If this wave is transmitted at 10 kHz, what is its wavelength? 

 

5.      Bats can detect small objects such as insects that are of the size approximately on the order of a wavelength.  If bats emit a chirp at a frequency of 60 kHz and the speed of sound waves in air is 330 m/s what is the smallest size insect they can detect?  

 

6.      Ocean waves with a wavelength of 120 m are coming in at a rate of 8 per minute.  What is their speed? 

 

7.      If the breakers at a beach are separated by 5 m and hit shore with a frequency of 0.2 Hz, with what speed are they traveling? 

 

8.      An earthquake emits both S waves and P waves which travel at different speeds through the Earth.  A P-wave travels at 9000 m/s and an S-wave travels at 5000 m/s.  If P-waves are received at a seismic station 1 minute before an S-wave arrives, how far to the earthquake center?

 

 

 

GENERAL WAVE MOTION:

 

        Period:             T = time for complete wave to pass a point. T =1/f      (sec)

        Frequency       f = number of cycles (waves) per second.  f = 1/T   (hertz)

        Wavelength:   l = distance between identical points on adjacent waves. (m)

        Velocity:         V = f  *  l      for any periodic wave

 

TYPES OF WAVES:

Transverse Waves:           V ={ T / (m / l) }       (on string)

Longitudinal Waves:        V = (B / r)                (fluid or bulk solid)

                                                         V = (Y / r)               (for rod-like solid)

 

 

PHYSICS   -  REVIEW SHEET

 

1.  WAVE MOTION: Frequency: f = # waves/second  (measured in hz)

 

        Period:             T = time for complete wave to pass a point. T =1/f      (sec)

        Frequency       f = number of cycles (waves) per second.  f = 1/T   (hertz)

        Wavelength:   l = distance between identical points on adjacent  waves. (m)

        Velocity:         V = f *  l      for any periodic wave

 

2. General Wave Equation

Y = A sin[(2px/l) – (2pt/T)] ; where l = the wavelength and T = the period of the wave.

The equation may also be written as

Y = A sin[kx – wt] ; where k = (2p/l) ; and w = (2p/T)

 

3.  SIMPLE HARMONIC MOTION:           F = - K * X

          Frequency:                                                    f =  ( (K/M) )/2 p (hertz)

          Angular Frequency:                                    w = (K/M) = 2p f            (radians/sec)

          Period:                                                            T = (2 p) * (M/K) (sec)

 

          Equations of Motion:       Y  =  A sin (wt + f)

                                                     V  =  w A cos (wt + f) = Vmax cos (wt + f)

                                                     A = - w2A sin (wt + f) = - amax sin (wt + f)

 

4.  TYPES OF WAVES:

           Transverse Waves:           V = { T / (m / l) }                (on string)

           Longitudinal Waves:        V =  (B / d)                        (fluid or bulk solid)

                                                      V =  (Y / d)                             (for rod-like solid)

                                                                               

 

5.  STANDING WAVES:  superposition of waves of equal amplitude and frequency

                                         traveling in opposite directions.

                                          

a) nodes, anti-nodes

b) on string, in pipe (open/closed ends)

c) fundamental, 1st overtone, 2nd overtone, etc

 

6.  SOUND WAVES:

        Velocity in air:             v = (331.5 m/s + .61 m/s-oC * T)        (T=deg.C)
                            

        Intensity:                I = Power/Area (watts/sq. meter):  I = k / r2
   

        Loudness:                                L = 10 log(I / Io) (decibels)  &           Io=1x10-12   watt/m2
         

        Beats:                     f  = | f1 - f2 |          (hertz)
   

        Doppler Shift:       fo = fs [(V {+/-} Vo)/(V {-/+} Vs)]
            

        Shock Waves:      sin Q = V(sound) / V(object)   (As in, bow wave, sonic boom, whip crack, Cerenkov radiation)