Problem 4 - AP Physics 1 with 2 Practice Test 2nd

Question

Two tuning forks are vibrating simultaneously. One fork has a frequency of \(256 \mathrm{~Hz} ;\) the other, a frequency of \(280 \mathrm{~Hz}\). The number of pulsational beats per second heard will be (A) 256 (B) 536 (C) 1.1 (D) 24

Step-by-Step Solution

Answer

24. The correct option is (D).

Step 1: Understanding Pulsational Beats

The number of beats per second (pulsational beats) heard is equal to the absolute difference in the frequencies of the two tuning forks.

Step 2: Identify Frequencies

The frequencies given are 256 Hz and 280 Hz.

Step 3: Calculate the Difference

Find the absolute difference between 280 Hz and 256 Hz. This is calculated as \( 280 \text{ Hz} - 256 \text{ Hz} = 24 \text{ Hz} \)

Step 4: Interpret the Result

The absolute difference of 24 Hz represents the number of beats per second heard.

Step 5: Choose the Correct Option

The number of pulsational beats per second heard is 24, which corresponds to option (D).

Key Concepts

Beat Frequency

When you hear two sounds with slightly different frequencies at the same time, you will perceive a phenomenon known as beats. The beat frequency is the rate at which this loud-quiet-loud pattern repeats. To determine the beat frequency, you simply find the absolute difference between the frequencies of the two sounds.
For example, if you have two tuning forks vibrating at frequencies of 256 Hz and 280 Hz, the beat frequency is calculated as:
\( |280 \ \text{Hz} - 256 \ \text{Hz}| = 24 \ \text{Hz} \) This means you will hear 24 beats per second. Beats are important in music for tuning instruments and creating special sound effects.

Sound Waves

Sound is a type of mechanical wave that travels through a medium, usually air. These waves are longitudinal, meaning that particles of the medium move back and forth in the same direction as the wave travels.
Tuning forks create sound waves by vibrating. When a tuning fork's prongs move, they push and pull on the air around them, generating pressure waves. These waves spread out and, when they reach our ears, we perceive them as sound.
Some essential characteristics of sound waves include:

• **Frequency**: The number of waves that pass a point in one second, measured in Hertz (Hz).
• **Amplitude**: The height of the wave, which determines the loudness of the sound.
• **Wavelength**: The distance between two consecutive points of the wave in the same phase.
• **Speed**: How fast the wave travels through the medium, usually air.

Understanding these characteristics is crucial for grasping how beats and harmonic motion work.

Harmonic Motion

Harmonic motion refers to any periodic motion, such as the shaking of a tuning fork. In this type of motion, an object moves back and forth through an equilibrium position. For tuning forks, each prong vibrates symmetrically around its central position.
Harmonic motion has two key features:

• **Amplitude**: The maximum extent of the vibration from the equilibrium.
• **Frequency**: The number of complete vibrations per second.
• **Phase**: The specific stage in one cycle of motion at a given point in time.

These characteristics help describe how the two tuning forks interact to create beat frequencies.
When two tuning forks with nearly identical harmonic frequencies are struck simultaneously, they interfere with each other to create a pattern of alternating constructive and destructive interference. This interaction gives rise to the audible beats that we perceive. In the given exercise, the beat frequency is the direct result of this interaction.