Question

A trick from Victorian times was to listen to the pitch of a fly's buzz, reproduce the musical note on the piano, and say how many times the fly's wings had flapped in 1 s. If the fly's wings flap 200 times in one second, determine the period of the musical note.

Short answer

The period of the musical note is 0.005 seconds.

Step-by-step solution

Understanding the Meaning of Period

The period of a wave (or a flap in this case) is the time it takes for one complete cycle to occur. It's the inverse of the frequency.

Convert Wing Flaps to Frequency

The number of wing flaps per second is the frequency of the flaps. Given: 200 flaps/second. Thus, the frequency (f) is 200 Hz.

Calculate the Period Using Frequency

The formula for the period (T) is the inverse of the frequency. Use the formula: \[ T = \frac{1}{f} \] Given \( f = 200 \) Hz, the period \( T = \frac{1}{200} \) seconds.

Simplify the Period

Perform the division: \[ T = \frac{1}{200} = 0.005 \] seconds.

Key concepts

Frequency and Period Relationship

To understand the relationship between frequency and period, let's start with simple definitions. The frequency of a wave is the number of cycles or flaps that occur in one second. The period is the time it takes to complete one cycle or flap. They are inversely related. This means when the frequency (f) is higher, the period (T) is shorter, and vice versa. You can calculate the period if you know the frequency using the formula: \( T = \frac{1}{f} \). For instance, in the given problem, the fly's wings flap 200 times per second, so the frequency is 200 Hz. Using the formula, we find the period \( T = \frac{1}{200} \) = 0.005 seconds. By breaking down the problem, it becomes clear how the period and frequency work in tandem.

Wave Mechanics

Wave mechanics help us describe the behavior of waves, whether it's sound, light, or even flapping wings! Waves have important properties such as amplitude, wavelength, and frequency, which together dictate how they behave. Here, frequency and period are vital components of wave mechanics. When a fly flaps its wings, it generates air pressure waves. The frequency (how many flaps per second) gives us the data on how often the waves occur, while the period tells us the time it takes for one flap or cycle. By understanding these fundamental properties, we can predict how the wave (or flap) behaves in different environments.

Hertz (Hz)

Hertz (Hz) is the unit of frequency. It tells us how many cycles occur per second. Named after Heinrich Hertz, it's essential for measuring and understanding frequencies across diverse fields such as music, telecommunications, and physics. In our fly example, 200 Hz means the wings flap 200 times each second. Knowing the frequency in Hertz allows us to quickly determine the period of the flaps using the inverse relationship formula. This unit's simplicity enables scientists and engineers to describe and manipulate waves effectively, making it a cornerstone in wave mechanics.