SOLUTION TO STUDY GUIDE, SECTION 1.6 SELECT PROBLEMS
20. A radio station broadcasts at a frequency of 107.9 megahertz (MHz). Hz=cycles/second.
a. How many seconds per cycle are there in 107.9 MHz?
ANALYSIS: IF 1 hertz = 1 cycle/second, THEN 1 megahertz = 106 cycles/second
The frequency is therefore 107.9 x 106 cycles/second
107.9 x 106 cycles .
1 second
OR
BUT we want seconds/cycle, so we must invert our fraction…
SOLUTION:
1 second
107.9 x 106 cycles
= 1 x 10-6 seconds/cycle
107.9
= 0.009267841 x 10-6 seconds/cycle
ANSWER = 9.268 x 10-9 seconds/cycle (4 sig figs)
b. What is the broadcast frequency in gigahertz?
ANALYSIS:
We are converting from 1 frequency (MHz) to another (GHz). Even though frequency is a combined unit
of measurement (cycles/second), we will use Hz b/c it is simpler.
CONVERSION EQUIVALENCIES: 1 GHz = 109 Hz
1 MHz = 106 Hz
GIVEN
CONV.FACTOR#1
CONV. FACTOR #2
↓
↓
↓
6
107.9MHz x
10 Hz
x
1GHz
1 MHz
109 Hz
= 107.9 x 106 GHz
109
ANSWER = 0.1079 GHz
OR 1.079 x 10-1 GHz
=
UNKNOWN
↓
______GHz
22. 120,000 calories
1 oz
x
4.184 J
1 calorie
= 502,080 J/oz
ANSWER = 5.0 x 10 5 J/oz (2 sig figs)
23. 5.0 x 105 J
1 oz
x
1 calorie
4.184 J
x
1 Calorie
1000 calories
x
1 oz
20T
x 1 T = ____ Calories
3t
t