What is the relationship between frequency and period?

What is the relationship between frequency and period?

• A. Frequency equals mass divided by period
• B. Frequency is the square of the period
• C. Frequency is the reciprocal of the period
• D. Frequency and period are unrelated

Answer: (C)

The relationship between frequency and period is fundamental in understanding oscillatory motion and wave phenomena. Frequency refers to how often an event occurs in a unit of time, typically expressed in hertz (Hz), which represents cycles per second. The period, on the other hand, is the duration of one complete cycle of the event, measured in seconds. The key connection between frequency and period is that they are inversely related. Specifically, frequency is defined as the reciprocal of the period. Mathematically, this relationship can be expressed with the following formula: \[ f = \frac{1}{T} \] where \( f \) is the frequency and \( T \) is the period. This means that if you know the period of an oscillating system, you can easily calculate its frequency by taking the reciprocal, and vice versa. Since the frequency measures how many cycles occur in one second, a longer period corresponds to fewer cycles in that same timeframe, thereby resulting in a lower frequency. Similarly, a shorter period means more cycles can fit into one second, leading to a higher frequency. This understanding is essential for analyzing various physical phenomena, including sound waves, light waves, and any periodic motion in mechanics.

The relationship between frequency and period is fundamental in understanding oscillatory motion and wave phenomena. Frequency refers to how often an event occurs in a unit of time, typically expressed in hertz (Hz), which represents cycles per second. The period, on the other hand, is the duration of one complete cycle of the event, measured in seconds.

The key connection between frequency and period is that they are inversely related. Specifically, frequency is defined as the reciprocal of the period. Mathematically, this relationship can be expressed with the following formula:

[ f = \frac{1}{T} ]

where ( f ) is the frequency and ( T ) is the period. This means that if you know the period of an oscillating system, you can easily calculate its frequency by taking the reciprocal, and vice versa.

Since the frequency measures how many cycles occur in one second, a longer period corresponds to fewer cycles in that same timeframe, thereby resulting in a lower frequency. Similarly, a shorter period means more cycles can fit into one second, leading to a higher frequency.

This understanding is essential for analyzing various physical phenomena, including sound waves, light waves, and any periodic motion in mechanics.