Amplitude, Time Period, And Frequency Of A Vibration

Key Notes :

Understanding Vibrations

• Vibration is the rapid back-and-forth movement of an object.
• Examples: A guitar string vibrating after being plucked, or a tuning fork set into motion.

Amplitude

• Definition: The amplitude is the maximum distance an object moves from its resting (mean) position during vibration.
• Represents the height of the wave produced by the vibration.
• Higher amplitude means louder sound (for sound waves) or more energy.
• Example: In a swinging pendulum, the amplitude is the maximum distance it swings away from its resting position.

Time Period

• Definition: The time period is the amount of time it takes for one complete cycle of vibration.
• Measured in seconds (s).
• Formula:

Time Period (T) = 1 / Frequency

• Example: If a pendulum takes 2 seconds to complete one swing, its time period is 2 seconds.

Frequency

• Definition: The frequency is the number of complete vibrations or cycles that occur in one second.
• Measured in hertz (Hz).
• Formula:

Frequency (f) = 1 / Time Period

• Higher frequency means a higher-pitched sound or faster vibration.
• Example: If a tuning fork vibrates 500 times per second, its frequency is 500 Hz.

Relationship Between Amplitude, Time Period, and Frequency

• Amplitude affects the loudness (for sound) but does not influence the frequency.
• Time period and frequency are inversely related: when one increases, the other decreases.
• The energy of a vibration increases with higher amplitude but remains unaffected by changes in frequency.

Real-Life Examples

• Musical instruments: The pitch of a note depends on the frequency of vibrations, while the loudness depends on the amplitude.
• Seismographs: Detect the vibrations of the Earth to measure earthquake intensity using amplitude.
• Clock pendulums: Operate on the principle of time period to keep accurate time.

Key Formulas

• Time Period: T = 1 / f​
• Frequency: f = 1 / T

Let’s practice!