Understanding Sound Wave Frequency and Time Period Relation

In physics, particularly when studying waves like sound waves, two important characteristics are frequency and time period. Understanding how they relate helps us describe the wave's behavior.

Defining Frequency (f)

Frequency represents how often a repeating event occurs within a specific time frame. For a sound wave, it's measured as the number of complete cycles (compressions and rarefactions) that pass a given point per second. The standard unit for frequency is Hertz (Hz), where 1 Hz equals one cycle per second.

Defining Time Period (T)

The time period, denoted by T, is the time it takes for one complete cycle of the wave to occur. It's essentially the duration of one oscillation or vibration. The unit for time period is seconds (s).

The Core Relation Between Frequency and Time Period

Frequency and time period are inversely related. This means that if one increases, the other decreases, and vice versa.

• If a wave completes many cycles in one second (high frequency), then the time taken for each cycle (time period) must be very short.
• Conversely, if a wave takes a long time to complete one cycle (long time period), then fewer cycles will pass in one second (low frequency).

This inverse relationship is mathematically expressed by the following formula:

$f = \frac{1}{T}$

Where:

• f is the frequency
• T is the time period

This formula clearly shows that frequency is the reciprocal of the time period.

Analyzing the Options

Let's look at why the other options are not correct:

• Option 1: $f = T$ - This suggests frequency and time period are equal, which contradicts their inverse relationship.
• Option 3: $f = T/2$ - This implies a specific fixed ratio that doesn't hold true for the general relationship between frequency and time period.
• Option 4: $f = 2T$ - Similar to option 3, this suggests a fixed multiplicative relationship, which is incorrect.
• Option 2: $f = 1/T$ - This accurately represents the inverse relationship where frequency is the reciprocal of the time period.

Therefore, the correct relation between the frequency (f) and time period (T) of a sound wave is $f = 1/T$.