# Physics 212, Quiz #6a: Jan 4, 1998

Show all work -- you may receive partial credit!

Fred is standing outside the SAU when an earthquake hits the RIT campus, coming from the east. Looking towards the dorms (1/4 mile = 0.4 km away), Fred sees ripples in the walkway, coming towards him.

Question 1: Is this a transverse or longitudinal wave?

```  Answer: Since the ripples are visible to Fred, they must be in the
vertical plane -- up and down.  The wave is travelling
east to west, perpendicular to the displacement.

-> transverse
```

The first ripple reaches him 1.5 seconds after it first appeared at the dorms.

Question 2: What is the speed of the wave?

```  Answer: the wave travels 400 meters in 1.5 seconds

400 meters
speed = -------------- = 267 m/s
1.5 sec
```

Just before the first crest reaches him, he can see 4 other crests in the walkway behind it.

Question 3: What is the wavelength of the wave?

```  Answer: there are two ways to interpret this question (my mistake).
One way is to imagine that, just as one crest reaches
Fred, he can see three others, plus one more _just_ exactly
at the dorm.  In that case, 4 crests span the entire distance

400 m
-> wavelength = ----------- = 100 m
4 crests

The other way to interpret the question is to imagine that,
just as one crest reaches Fred, he can see clearly 4 other
crests in the walkway between himself and the dorm.
There could be a fifth crest _just_ about to emerge from
under the dorm.  In this case,

400 m
-> wavelength = ----------- = 80 m
5 crests

I accepted any answer between these two limits.
```

The crest of the wave raises Fred 30 cm above its trough.

Question 4: What is the amplitude of the wave?

```  Answer: the amplitude is the maximum displacement of the wave
from the rest position.  The distance crest-to-rest is
one amplitude, and the distance rest-to-trough is also
one amplitude; thus, crest-to-trough is two times the
amplitude

amplitude A = 0.5 * 30 cm = 15 cm
```

Question 5: The earthquake lasts for 10 seconds. How many times is Fred raised upwards during that span of time?

```  Answer: the frequency of a wave is the number of times per second
that wave crests pass a fixed point.  If the frequency of
the wave is "f", Fred will be raised upwards "f" times each
second.  In 10 seconds, he'll be raised upwards 10*f times.

speed of wave
frequency f = -------------
wavelength

267 m/s
if wavelength = 100 m,    f = ------- = 2.67 cycles/sec
100 m

-> Fred raised (10 sec)*(2.67 cycles/sec) = 26.7 times

267 m/s
if wavelength = 80 m,     f = ------- = 3.33 cycles/sec
80 m

-> Fred raised (10 sec)*(3.33 cycles/sec) = 33.3 times

```

Question 6: Write an equation which describes Fred's height above the walkway's level as a function of time.

```  Answer: The equation of simple harmonic motion describes the displacement
as a function of time:

height =   A * sin(2*pi*f*t)

where
A = amplitude of wave = 15 cm
f = frequency of wave = 2.67 cycles/sec  or
3.33 cycles/sec

One can also define

omega = 2*pi*f   = 20.9 radians/sec or

and write
height =   A * sin(omega*t)

One can also write
2*pi*t
height =   A * sin(------)
T

where
T = period of wave    = 0.30 seconds  or
0.38 seconds

In order to get credit for this question, a student had to
write the equation as above, _and_ define (here or earlier)
the numerical values of "A" and "f" (or "T").
```