Question

Identify which of the properties is equal to the reciprocal of the Time period?
I)Speed
II)Wavelength
III)Frequency
$(A)$ I only
$(B)$ II only
$(C)$III only
$(D)$ II and III only
$(E)$ I, II, and III

Answer 1

Hint: The definition of speed, wavelength, and frequency have to be known. From the definitions, the relations between these quantities with time can be evaluated. Speed is the rate of change of the distance in unit time so it depends upon time. The wavelength can be defined by the gap between troughs of waves. Frequency is the number of vibrations per unit time by a particle in a periodic motion.
Formula used:
Speed $v={\displaystyle \frac{d}{t}}$ $d$is the total path cross by an object in time $t$
Frequency $n={\displaystyle \frac{1}{T}}$ $T$is time-period.

Complete step by step answer:
The given properties are speed, wavelength, and frequency. Among these, we have to found the quantities which are reciprocal of the time period. Let us define these properties.
Speed: Speed is defined by the total path cross by an object in a certain time. If an object crosses the total path $d$ in time $t$ , Speed $v={\displaystyle \frac{d}{t}}$.
Clearly, speed has an inverse relationship with time, but not the reciprocal of time.
Wavelength: The wavelength is the measurement of the distance between the two peaks of a wave. It is just a length and not dependent upon time.
Frequency: The frequency is the number of vibrations or cycle per unit time period. Whereas, the time period is defined by the seconds per unit cycle.
Frequency $n={\displaystyle \frac{1}{T}}$ $T$is time-period.
Hence, the frequency is the reciprocal of the time period.
Hence, option C is correct.

Note: A complete vibration or a complete cycle is defined by the phenomena in which a vibrated particle starts from a point on its way of journey and comes back to the same point with the motion.
The time period is the time taken by a particle for a complete vibration or oscillation. Its unit is second.
The frequency is the number of complete oscillations or vibrations per unit time period. It is measured in Hz units. $1Hz=\sec$