Calculate the frequency of each of the following values of period (acceptable units are $$ \mathrm{Hz}, \mathrm{kHz} $$, or MHz ): $$ \begin{aligned} ext { 1. } \mathrm{T} & =37 \mathrm{~s} \ \mathrm{f} & =\square \ ext { 2. } \mathrm{T} & =40 \mathrm{~ms} \ \mathrm{f} & =\square \ ext { 3. } \mathrm{T} & =19 \mu \mathrm{~s} \ \mathrm{f} & =\square\end{aligned} $$

Question

Calculate the frequency of each of the following values of period (acceptable units are $$ \mathrm{Hz}, \mathrm{kHz} $$, or MHz ): $$ \begin{aligned} 	ext { 1. } \mathrm{T} & =37 \mathrm{~s} \ \mathrm{f} & =\square \ 	ext { 2. } \mathrm{T} & =40 \mathrm{~ms} \ \mathrm{f} & =\square \ 	ext { 3. } \mathrm{T} & =19 \mu \mathrm{~s} \ \mathrm{f} & =\square\end{aligned} $$

UpStudy AI · Accepted Answer

**1. For $$ T = 37 \, \mathrm{s} $$:**

- The relationship between period and frequency is  
  $$
  f = \frac{1}{T}
  $$
  
- Substitute $$ T = 37 \, \mathrm{s} $$:
  $$
  f = \frac{1}{37} \approx 0.027 \, \mathrm{Hz}
  $$

---

**2. For $$ T = 40 \, \mathrm{ms} $$:**

- First, convert milliseconds to seconds:
  $$
  40 \, \mathrm{ms} = 40 \times 10^{-3} \, \mathrm{s} = 0.04 \, \mathrm{s}
  $$
  
- Now, compute the frequency:
  $$
  f = \frac{1}{0.04} = 25 \, \mathrm{Hz}
  $$

---

**3. For $$ T = 19 \, \mu\mathrm{s} $$:**

- Convert microseconds to seconds:
  $$
  19 \, \mu\mathrm{s} = 19 \times 10^{-6} \, \mathrm{s}
  $$
  
- Calculate the frequency:
  $$
  f = \frac{1}{19 \times 10^{-6}} \approx 52631.6 \, \mathrm{Hz}
  $$
  
- To express the frequency in kilohertz ($$ \mathrm{kHz} $$):
  $$
  52631.6 \, \mathrm{Hz} = \frac{52631.6}{1000} \approx 52.63 \, \mathrm{kHz}
  $$

---

**Final Answers:**

1. $$ T = 37 \, \mathrm{s} $$  $$ f \approx 0.027 \, \mathrm{Hz} $$
  
2. $$ T = 40 \, \mathrm{ms} $$  $$ f = 25 \, \mathrm{Hz} $$
  
3. $$ T = 19 \, \mu\mathrm{s} $$  $$ f \approx 52.63 \, \mathrm{kHz} $$
1. $$ T = 37 \, \mathrm{s} $$  $$ f \approx 0.027 \, \mathrm{Hz} $$ 2. $$ T = 40 \, \mathrm{ms} $$  $$ f = 25 \, \mathrm{Hz} $$ 3. $$ T = 19 \, \mu\mathrm{s} $$  $$ f \approx 52.63 \, \mathrm{kHz} $$

Calculate the frequency of each of the following values of period (acceptable units are , or MHz ):

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