Question

An automobile wheel of diameter $0.50 \mathrm{m}$ is found to emit sound with a frequency of $10 \mathrm{Hz}$. What is the automobile's speed? Hint: Assume the frequency of the emitted sound is equal to the rotation frequency of the wheel.

Name: Problem 12, Chapter 13: College Physics: Reasoning and Relationships
Uploaded: 2022-02-12T18:33:10-08:00
Duration: 56 s
Channel: Mirza Aslam Beig
Description: An automobile wheel of diameter 0.50 m is found to emit sound with a frequency of 10 Hz. What is the automobile's speed? Hint: Assume the frequency of the emitted sound is equal to the rotation frequency of the wheel.

   An automobile wheel of diameter $0.50 \mathrm{m}$ is found to emit sound with a frequency of $10 \mathrm{Hz}$. What is the automobile's speed? Hint: Assume the frequency of the emitted sound is equal to the rotation frequency of the wheel.

College Physics: Reasoning and Relationships

Nicholas J.… 2nd Edition

Chapter 13, Problem 12

Instant Answer

Solved by Expert Mirza Aslam Beig

02/12/2022

Step 1

The radius (r) of a circle is half of its diameter (d). So, we can write this as: \[ r = \frac{d}{2} \] Substituting the given diameter (d = 0.50 m) into the equation, we get: \[ r = \frac{0.50 \, \text{m}}{2} = 0.25 \, \text{m} \] Show more…

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An automobile wheel of diameter $0.50 \mathrm{m}$ is found to emit sound with a frequency of $10 \mathrm{Hz}$. What is the automobile's speed? Hint: Assume the frequency of the emitted sound is equal to the rotation frequency of the wheel.

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Key Concepts

Rotational Frequency

Rotational frequency is the number of complete rotations that occur per unit time. It is a fundamental concept in rotational kinematics, linking periodic motion to time, and in this context, it denotes how many times the wheel rotates in one second.

Wheel Circumference

The wheel circumference is the distance around the edge of the wheel and can be calculated using its diameter or radius. This measurement is crucial because it represents the distance traveled by the vehicle with each full rotation of the wheel.

Relationship Between Rotational Motion and Linear Speed

The relationship between rotational motion and linear speed is established by the fact that the distance a rotating object travels is the product of its rotation frequency and its circumference. This concept allows one to calculate the vehicle's linear speed by multiplying the number of rotations per unit time by the distance covered per rotation.

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