Question

The frequency range of audible sound for humans is 20Hz and 20000Hz. Find the corresponding range of time periods for these audible sounds.
A) 0.05s to $5\times {10}^{-5}s$
B) 0.5s to $5\times {10}^{-5}s$
C) 5s to $5\times {10}^{-5}s$
D) 0.05s to $2.5\times {10}^{-5}s$

Answer 1

Hint: Frequency is inversely proportional to period. The frequency of a wave increases and the period of the wave decreases. The frequency below 20Hz is known as infrasound which is not audible to the human ear whereas the frequency above 20000Hz is known as ultrasound which is also not audible to human ears.

Formula used:
To solve this type of question we use the following formula.
$T={\displaystyle \frac{1}{f}}$
Where $T$ is time and $f$ is frequency.

Complete step by step answer:
Let us first write the information given in the question.
The audible sound frequency range for humans is 20Hz and 20000Hz.
Now let us convert the frequency into time period using the following formula.
$T={\displaystyle \frac{1}{f}}$
Let us convert 20Hz in periods.
$\Rightarrow T={\displaystyle \frac{1}{20}}=0.05s$
Similarly, let us convert 20000Hz in the time.
$\Rightarrow T={\displaystyle \frac{1}{20000}}=5\times {10}^{-5}s$
Therefore, the period range of audible frequency is 0.05s and $5\times {10}^{-5}s$.

Hence, Option (A) is correct.

Additional Information:
Doppler Effect is an important phenomenon about hearing. The speed of stars and galaxies is measured by the Doppler effect. There are two mechanisms in the Doppler effect named a red shift and blue shift.

Note:
- A time period T is defined as the time is taken for one complete cycle of vibration to pass a given point.
- The SI unit of the period is 'seconds'.
- Wave frequency is the number of waves that pass through a fixed point in a given period.
- The SI unit of frequency is Hertz.