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11. A string vibrates at a frequency of 15 Hz. What is its period?

12. A speaker vibrates at a frequency of 292 Hz. What is its period?

13. A swing has a period of 12 seconds. What is its frequency?

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]