Question

Calculate the period and frequency for the seconds hand ,minute hand and hour hand of a clock .

Answer 1

Step 1: Given data .

1 hour =60 minutes .

1 minute = 60 seconds.

Step 2: Formulas Required .

Frequency is the number of oscillations/cycles/vibrations per unit time .

Frequency ( f ) = $\frac{no.ofcycles}{time}$hertz.

Frequency and time period are inversely proportional to each other .

Time period= $\frac{1}{f}$ seconds.

Step 3: Calculations.

For seconds hand

Time period =1 minute = 60 seconds .

Frequency ( f ) = $\frac{no.ofcycles}{time}$hertz , or reciprocal of time .

f = $\frac{1}{tseconds}$.

f= $\frac{1}{60}=0.01667Hz$.

For minutes hand .

Time period =1 hour = 60 minutes or 3600 seconds .

Frequency ( f ) = $\frac{1}{tseconds}$.

f = $\frac{1}{3600seconds}=0.000277777778Hz$ or

f = $2.77\times {10}^{-4}Hz$.

For Hours hand .

Time period = 12 hours =$12\times 3600=43,200seconds$.

Frequency ( f ) = $\frac{1}{tseconds}$.

f=$$\begin{gathered} \frac{1}{43,200seconds} \\ f=2.3\times {10}^{-5}Hz. \end{gathered}$$

Hence,

For seconds hand ,Time period =1 minute =60 seconds and f =0.01667 Hz

for minutes hand ,Time period =1 hour = 60 minutes or 3600 seconds and f = $2.77\times {10}^{-4}Hz$.

for hours hand , Time period = 43,200 seconds and f = $2.3\times {10}^{-5}Hz$.