When a guitar string plays the note 'A,' the string vibrates at 440 Hz. What is the period of the vibration?

Verified step by step guidance

1. Understand the relationship between frequency and period. The period (T) is the reciprocal of the frequency (f). This relationship is expressed as: $T=\frac{1}{f}$.
2. Identify the given value in the problem. The frequency of the vibration is provided as 440 Hz.
3. Substitute the given frequency value into the formula: $T=\frac{1}{440}$.
4. Simplify the fraction to calculate the period. This will give the time it takes for one complete vibration of the string.
5. Express the result in seconds (s), as the period is a measure of time. Ensure the units are consistent and appropriate for the context of the problem.

Key Concepts

Frequency

Frequency is the number of cycles of a periodic wave that occur in one second, measured in hertz (Hz). In this context, the guitar string vibrates at a frequency of 440 Hz, meaning it completes 440 cycles of vibration every second. Understanding frequency is essential for relating it to other wave properties, such as period.

Period

The period of a wave is the duration of one complete cycle of vibration, typically measured in seconds. It is the reciprocal of frequency, meaning that the period (T) can be calculated using the formula T = 1/f, where f is the frequency. For the guitar string vibrating at 440 Hz, the period indicates how long it takes for one complete vibration to occur.

Wave Properties

Wave properties encompass various characteristics of waves, including frequency, period, amplitude, and wavelength. These properties are interrelated; for instance, knowing the frequency allows us to determine the period, and vice versa. Understanding these properties is crucial for analyzing sound waves produced by musical instruments like guitar strings.