Question

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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?

Answer 1

`\qquad\qquad\huge\underline{{\sf Answer}}`

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 :

`\qquad \sf  \dashrightarrow \: frequency = (1)/(period)`

Now, let's move on to problems ~

# 11. f = 15 hertz, t = ?

`\qquad \sf  \dashrightarrow \: t = (1)/(15) \: \: sec`

`\qquad \sf  \dashrightarrow \: t \approx0.067 \: \: sec`

#12. f = 292 hertz, t = ?

`\qquad \sf  \dashrightarrow \: t = (1)/(292) \: \: sec`

`\qquad \sf  \dashrightarrow \: t \approx0.0034 \: \: sec`

#13. t = 12 seconds, f = ?

`\qquad \sf  \dashrightarrow \: f= (1)/(12) \: \: hertz`

`\qquad \sf  \dashrightarrow \: f \approx0.083 \: \: hertz`

Answer 2

`\huge\underline{\underline{\mathbb{A\:N\:S\:W\:E\:R}}}`

We know that, frequency = reciprocal of the period of time an object swings or vibrates at. Therefore,

`\tt\:FORMULA \downarrow\\\\\star\boxed{\mathfrak{Frequency = (1)/(period \: of \: time)}}`

Now, let's solve the questions by using this formula.

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11. Frequency = 15 Hz

Period = ?

`\sf\:Frequency = (1)/(period)\\\sf\:15 = (1)/(period)\\\boxed{\bf\:period = (1)/(15) = 0.67 \: s}`

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12. Frequency = 292 Hz

Period = ?

`\sf\:Frequency = (1)/(period)\\\sf\:292 = (1)/(period)\\\boxed{\bf\:period = (1)/(292) = 0.0034 \: s}`

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13. Period = 12 s

Frequency = ?

`\sf\:Frequency = (1)/(period)\\\sf\:Frequency = (1)/(12)\\\boxed{\bf\:Frequency = 0.083 \: Hz}`

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Note:

The SI units of,

• Frequency = Hertz (Hz)
• Period of time = Second (s / sec)

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