Problem 8 - Applied Physics

Question

A wave generator produces 20 pulses in \(3.50 \mathrm{~s}\). (a) What is its period? (b) What is its frequency?

Step-by-Step Solution

Answer

Frequency: 5.71 Hz, Period: 0.175 s.

Step 1: Identify the Given Information

The wave generator produces 20 pulses in 3.50 seconds. We need to find the period and frequency of the wave.

Step 2: Calculate Frequency

The frequency is the number of pulses (or cycles) per unit time. It can be calculated using the formula \( f = \frac{N}{t} \), where \( N = 20 \) pulses and \( t = 3.50 \) seconds. Thus, \( f = \frac{20}{3.50} \approx 5.71 \) Hz.

Step 3: Calculate Period

The period \( T \) is the reciprocal of the frequency \( f \). It represents the time for one complete cycle. Using the formula \( T = \frac{1}{f} \), we find \( T \approx \frac{1}{5.71} \approx 0.175 \) s.

Key Concepts

Wave Period

The wave period, often denoted as \( T \), is a fundamental concept in wave physics. It represents the duration required for one complete cycle of a wave to pass a given point. Essentially, the period is the wave's heartbeat, dictating how long it takes for the wave to "start over".

In simpler terms, if you think of waves at the beach, the wave period is the time between one wave crest hitting your feet to the next crest reaching the same spot. It's a measure of time, expressed in seconds (s), highlighting that each wave cycle is an event that takes time to unfold.

To find the period of a wave, we use the formula \( T = \frac{1}{f} \), where \( f \) is the frequency of the wave. The wave period and frequency are inversely related, meaning if one increases, the other decreases.

• Small period values indicate fast-repeating cycles.
• Large period values suggest slow cycles.

Understanding the wave period helps in predicting and analyzing phenomena like sound waves or electromagnetic waves, which are crucial in various technologies and natural processes.

Wave Frequency

Wave frequency, denoted as \( f \), is a vital aspect of understanding waves. It defines how many wave cycles occur in one second, indicating the wave's pace or energy. Frequency tells you how "frequent" these cycles are.

Measured in hertz (Hz), frequency is calculated using the formula \( f = \frac{N}{t} \), where \( N \) is the number of cycles (or pulses), and \( t \) is the time in seconds. In our particular scenario, the wave generator output 20 pulses over 3.50 seconds, which gives us a frequency of about 5.71 Hz.

High frequencies reflect rapid cycles and are often associated with sounds or light at higher pitches or energies. Conversely, low frequencies correspond to slow, deep cycles, like a bass sound or red light. Frequency is essential for understanding wave behavior, whether it's tuning a radio or using a microwave.

• High frequency = short period.
• Low frequency = long period.

Frequency provides insight into many technological applications, like communication signals or musical notes, making it a cornerstone of wave physics.

Pulse Generator

A pulse generator is an intriguing device in the realm of wave physics. It is designed to produce a consistent and controlled series of pulses or waveforms. Think of it as a machine that crafts regular, repeating signals with precision.

Pulse generators are crucial in various scientific experiments and technological applications. They help create synchronized timing signals in electronic circuits and communication systems. Imagine needing a perfectly timed beep repeatedly; a pulse generator handles this seamlessly.

The functionality of a pulse generator centers around adjusting both the frequency and period of the pulses. This adjustability is key to their versatility, allowing them to be tailored for different scenarios.

• Can simulate different waveforms.
• Used in laboratories for testing and calibrations.

By understanding how a pulse generator works, users can harness it to emulate various wave conditions, essential for designs and diagnostic processes across many fields.