Respuesta :
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
As we know, period (t)of a wave and it's frequency (f) are Reciprocal of each other, so if one is know then we can just reverse the order to get the other one.
that is :
[tex]\qquad \sf \dashrightarrow \: frequency = \dfrac{1}{period} [/tex]
Now, let's move on to problems ~
# 11. f = 15 hertz, t = ?
[tex]\qquad \sf \dashrightarrow \: t = \dfrac{1}{15} \: \: sec[/tex]
[tex]\qquad \sf \dashrightarrow \: t \approx0.067 \: \: sec[/tex]
#12. f = 292 hertz, t = ?
[tex]\qquad \sf \dashrightarrow \: t = \dfrac{1}{292} \: \: sec[/tex]
[tex]\qquad \sf \dashrightarrow \: t \approx0.0034 \: \: sec[/tex]
#13. t = 12 seconds, f = ?
[tex]\qquad \sf \dashrightarrow \: f= \dfrac{1}{12} \: \: hertz[/tex]
[tex]\qquad \sf \dashrightarrow \: f \approx0.083 \: \: hertz[/tex]
[tex]\huge\underline{\underline{\mathbb{A\:N\:S\:W\:E\:R}}}[/tex]
We know that, frequency = reciprocal of the period of time an object swings or vibrates at. Therefore,
[tex]\tt\:FORMULA \downarrow\\\\\star\boxed{\mathfrak{Frequency = \frac{1}{period \: of \: time}}}[/tex]
Now, let's solve the questions by using this formula.
[tex]\rule{150pt}{2pt}[/tex]
11. Frequency = 15 Hz
Period = ?
[tex]\sf\:Frequency = \frac{1}{period}\\\sf\:15 = \frac{1}{period}\\\boxed{\bf\:period = \frac{1}{15} = 0.67 \: s}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
12. Frequency = 292 Hz
Period = ?
[tex]\sf\:Frequency = \frac{1}{period}\\\sf\:292 = \frac{1}{period}\\\boxed{\bf\:period = \frac{1}{292} = 0.0034 \: s}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
13. Period = 12 s
Frequency = ?
[tex]\sf\:Frequency = \frac{1}{period}\\\sf\:Frequency = \frac{1}{12}\\\boxed{\bf\:Frequency = 0.083 \: Hz}[/tex]
[tex]\rule{150pt}{2pt}[/tex]
Note:
The SI units of,
- Frequency = Hertz (Hz)
- Period of time = Second (s / sec)
[tex]\rule{150pt}{2pt}[/tex]