/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 102 Two cars are moving towards each... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 102

Two cars are moving towards each other with same speed, if frequency of horn blown by driver of one car and frequency appeared to another driver differ by \(4 \%\) from the frequency of horn, then find out speed of cars (speed of sound \(=300 \mathrm{~m} / \mathrm{s}\) ) (A) \(12 \mathrm{~m} / \mathrm{s}\) (B) \(6.6 \mathrm{~m} / \mathrm{s}\) (C) \(4.2 \mathrm{~m} / \mathrm{s}\) (D) \(5.9 \mathrm{~m} / \mathrm{s}\)

Short Answer

Expert verified
The speed of the cars is approximately \(5.9 \mathrm{~m} / \mathrm{s}\), which corresponds to answer choice (D).

Step by step solution

01

Understand the Doppler Effect formula

The formula for the Doppler Effect when the source and observer are moving towards each other can be given as: \(f' = f (\frac{v + v_o}{v - v_s})\) where: - \(f'\) is the observed frequency - \(f\) is the actual frequency of the horn - \(v\) is the speed of sound given as 300 m/s - \(v_o\) is the speed of the observer (the driver of one car) - \(v_s\) is the speed of the source (the driver of the other car) Since both cars are moving towards each other with an equal speed, we can set \(v_o = v_s = v_c\). The formula becomes: \(f' = f (\frac{v + v_c}{v - v_c})\)
02

Use the given information to set up the equation

We're given that the apparent frequency differs by \(4\%\) from the actual frequency. So, we can write: \(f' = 1.04 f\) Now, substitute the Doppler Effect formula: \(1.04 f = f(\frac{v + v_c}{v - v_c})\)
03

Solve for the speed of the cars

We can rearrange the equation to isolate the term \(v_c\): \(1.04 = \frac{v + v_c}{v - v_c}\) Next, cross-multiply: \(1.04(v - v_c) = v + v_c\) Expand and simplify: \(1.04v - 1.04v_c = v + v_c\) Rearrange the equation to isolate \(v_c\): \(v_c(1.04+1) =1.04v - v\) Divide by 2.04: \(v_c = \frac{(1.04 - 1)v}{2.04}\) Now, we plug in the given value of the speed of sound: \(v_c = \frac{(1.04 - 1)(300)}{2.04} = \frac{(0.04)(300)}{2.04}\) Finally, solve for \(v_c\): \(v_c \approx 5.9 \mathrm{~m} / \mathrm{s}\) So, the speed of the cars is approximately \(5.9 \mathrm{~m} / \mathrm{s}\), which corresponds to answer choice (D).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Fig. \(9.40\), a block of mass \(M=1 \mathrm{~kg}\) is attached to one end of massless spring of spring constant \(k=100 \mathrm{~N} / \mathrm{m}\) and other end of spring is fixed. Initially, spring in its natural length. A horizontal force \(F=10 \mathrm{~N}\) at \(t=0\) is applied on the block. | Column-I | | :--- | | (A) Amplitude of SHM in cm is | | (B) Maximum speed of block in | | cm//s is | | (C) The time in second after which | | compression in the spring | | is half of amplitude if block | | starts from extreme position | | (D) Maximum compression in the | | spring in cm is |

A closed organ pipe of length \(L\) vibrating in second overtone, then match the following Column-I (A) Displacement node (B) Displacement anti-node (C) Pressure node (D) Pressure anti-node Column-II 1\. Closed end 2\. Open end 3\. \(4 L / 5\) from closed end 4\. \(L / 5\) from closed end

The length of a simple pendulum executing simple harmonic motion is increased by \(21 \%\). The percentage increase in the time period of the pendulum of increased length is (A) \(11 \%\) (B) \(21 \%\) (C) \(42 \%\) (D) \(10 \%\)

A book with many printing errors contains four different expressions for the displacement \(y\) of a particle executing SHM. Which of the following expressions are wrong? (A) \(y=A \sin \left(\frac{2 \pi t}{T}\right)\) (B) \(y=A \sin v t\) (C) \(y=\frac{A}{T} \sin \left(\frac{t}{A}\right)\) (D) \(y=\frac{A}{\sqrt{2}}(\sin \omega t+\cos \omega t)\)

A \(3.6 \mathrm{~m}\) long vertical pipe is filled completely with a liquid. A small hole is drilled at the base of the pipe due to which liquids starts leaking out. This pipe resonates with a tuning fork. The first two resonances occur when height of water column is \(3.22 \mathrm{~m}\) and \(2.34 \mathrm{~m}\), respectively. The area of cross-section of pipe is (A) \(25 \pi \mathrm{cm}^{2}\) (B) \(100 \pi \mathrm{cm}^{2}\) (C) \(200 \pi \mathrm{cm}^{2}\) (D) \(400 \pi \mathrm{cm}^{2}\)
See all solutions

Recommended explanations on Physics Textbooks

Wave Optics

Read Explanation

Rotational Dynamics

Read Explanation

Medical Physics

Read Explanation

Electricity

Read Explanation

Space Physics

Read Explanation

Measurements

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.