Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

A police car is chasing a speeding Porsche 911. Assume that the Porsche’s maximum speed is $80 .0 \frac{m}{s}$ and the police car’s is $54 .0 \frac{m}{s}$ . At the moment both cars reach their maximum speed, what frequency will the Porsche driver hear if the frequency of the police car’s siren is $440 Hz$ ? Take the speed of sound in air to be . $340 \frac{m}{s}$

The frequency heard by the Porsche driver is $400 Hz$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data

The maximum speed of Porsche is $v_{D} = 80.0 \frac{m}{s}$
The speed of the police car is $v_{s} = 54.0 \frac{m}{s}$
The frequency of the police car’s siren is $f = 440 Hz$
The speed of sound in air is $v = 340 \frac{m}{s}$

Step 2: Determine the concept of the Doppler Effect

Use the concept of the Doppler effect of sound. We can set the sign according to the rule. The detector is the Porsche’s driver and the source is the siren of the police car. If the detector moves away, then use the sign in the numerator to get a shift down which means the frequency would decrease. If the source moves towards the detector, use the minus sign in the denominator to get a shift up which means the frequency would increase.

Formula:

The frequency received by the observer or the source according to Doppler’s Effect, (observer moving away from source and source moving towards observer) $f' = f (\frac{v - v_{D}}{v - v_{s}})$ (i)

Step 3: Calculate the frequency heard by the Porsche driver

As, the driver is moving away from the police car and the police car is approaching the driver, the frequency of the wave heard by the driver is given using the equation (i) as:

$\begin{matrix} f^{'} = 440 Hz (\frac{340 \frac{m}{s} - 80.0 \frac{m}{s}}{340 \frac{m}{s} - 54.0 \frac{m}{s}}) \\ = 40 0 Hz \end{matrix}$

Hence, the frequency of the sound wave heard by the driver is $400 Hz$

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: The given data

Step 2: Determine the concept of the Doppler Effect

Step 3: Calculate the frequency heard by the Porsche driver

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: The given data

Step 2: Determine the concept of the Doppler Effect

Step 3: Calculate the frequency heard by the Porsche driver

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics