Question

The length of a minute hand of a clock is $4 \mathrm{cm}$. Find the displacement and average velocity of the tip of the minute hand when it moves during a time interval from 3: $15 \mathrm{pm}$ to $3: 30 \mathrm{pm} ?$

Answer 1

Hint: We can say that frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency and angular frequency. Frequency is measured in units of hertz (Hz) which is equal to one occurrence of a repeating event per second. Frequency measures the number of times something occurs in a specific amount of time. While frequency can be used to measure the rate of any action, in technical applications it is typically used to measure wave rates or processing speed.

Complete step by step answer
We know that a time period (denoted by 'T’) is the time taken for one complete cycle of vibration to pass a given point. As the frequency of a wave increases, the time period of the wave decreases. The unit for time period is 'seconds'.

$\mathrm{l}=4 \mathrm{cm}$
The angle between the positions of $3.15 \mathrm{pm}$ to 3.30 is $90^{\circ}$
$\therefore$ displacement $=\sqrt{1^{2}+l^{2}}$
$=4 \sqrt{2} \mathrm{cm}$
Time $=15$ min
Average velocity $=\dfrac{\text { displacement }}{\text { total time taken }}$
$=\dfrac{4 \sqrt{2} \mathrm{cm}}{15 \times 60 \mathrm{s}}=\dfrac{\sqrt{2}}{225} \mathrm{cms}^{-1}$

Note We know that wave frequency is the number of waves that pass a fixed point in a given amount of time. The SI unit for wave frequency is the hertz (Hz), where 1 hertz equals 1 wave passing a fixed point in 1 second. T is the time it takes for one complete oscillation; it is measured in seconds. All waves, including sound waves and electromagnetic waves, follow this equation. For example, a wave with a time period of 2 seconds has a frequency of 1/ 2 = 0.5 Hz. A sound wave has a time period of 0.0001 seconds.