/*! 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 39 A source of sound waves of frequ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Problem 39

A source of sound waves of frequency \(1.0 \mathrm{kHz}\) is stationary. An observer is traveling at 0.50 times the speed of sound. (a) What is the observed frequency if the observer moves toward the source? (b) Repeat if the observer moves away from the source instead.

Short Answer

Expert verified
Answer: The observed frequencies are 1.5 kHz when the observer moves towards the source, and 0.5 kHz when the observer moves away from the source.

Step by step solution

01

Identify the Doppler Effect Formula

The Doppler effect formula for sound waves is given by: $$f_{obs} = f_{src} \frac{v \pm v_{obs}}{v \mp v_{src}},$$ where \(f_{obs}\) is the observed frequency, \(f_{src}\) is the source frequency, \(v\) is the speed of sound, \(v_{obs}\) is the observer's speed, and \(v_{src}\) is the source's speed. In our case, the source is stationary, so \(v_{src} = 0\). The observer's speed is 0.50 times the speed of sound, which can be represented as \(v_{obs} = 0.50v\). #Step 2: Calculate Observed Frequency when the Observer moves toward the source#
02

Calculate observed frequency when the observer moves toward the source

When the observer moves toward the source, we use the formula with the plus sign for the numerator and the minus sign for the denominator. Plugging in the given values, we get: $$f_{obs1} = (1.0 \mathrm{kHz}) \frac{v + 0.50v}{v - 0} = (1.0 \mathrm{kHz}) \frac{1.50v}{v}$$ We can simplify the expression: $$f_{obs1} = 1.5 \times (1.0 \mathrm{kHz}) = 1.5 \mathrm{kHz}$$ So, the observed frequency when the observer moves toward the source is 1.5 kHz. #Step 3: Calculate Observed Frequency when the Observer moves away from the source#
03

Calculate observed frequency when the observer moves away from the source

When the observer moves away from the source, we use the formula with the minus sign for the numerator and the plus sign for the denominator. Plugging in the given values, we get: $$f_{obs2} = (1.0 \mathrm{kHz}) \frac{v - 0.50v}{v + 0} = (1 \mathrm{kHz}) \frac{0.50v}{v}$$ We can simplify the expression: $$f_{obs2} = 0.5 \times (1.0 \mathrm{kHz}) = 0.5 \mathrm{kHz}$$ So, the observed frequency when the observer moves away from the source is 0.5 kHz. To summarize, the observed frequencies for the given situation are: (a) 1.5 kHz when the observer moves towards the source, and (b) 0.5 kHz when the observer moves away from the source.

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

At a baseball game, a spectator is \(60.0 \mathrm{m}\) away from the batter. How long does it take the sound of the bat connecting with the ball to travel to the spectator's ears? The air temperature is \(27.0^{\circ} \mathrm{C}\)
Find the speed of sound in mercury, which has a bulk modulus of $2.8 \times 10^{10} \mathrm{Pa}\( and a density of \)1.36 \times\( \)10^{4} \mathrm{kg} / \mathrm{m}^{3}.$
A source of sound waves of frequency \(1.0 \mathrm{kHz}\) is traveling through the air at 0.50 times the speed of sound. (a) Find the frequency of the sound received by a stationary observer if the source moves toward her. (b) Repeat if the source moves away from her instead.
Two tuning forks, \(A\) and \(B\), excite the next-to-lowest resonant frequency in two air columns of the same length, but A's column is closed at one end and B's column is open at both ends. What is the ratio of A's frequency to B's frequency?
A musician plays a string on a guitar that has a fundamental frequency of \(330.0 \mathrm{Hz}\). The string is \(65.5 \mathrm{cm}\) long and has a mass of \(0.300 \mathrm{g} .\) (a) What is the tension in the string? (b) At what speed do the waves travel on the string? (c) While the guitar string is still being plucked, another musician plays a slide whistle that is closed at one end and open at the other. He starts at a very high frequency and slowly lowers the frequency until beats, with a frequency of \(5 \mathrm{Hz}\), are heard with the guitar. What is the fundamental frequency of the slide whistle with the slide in this position? (d) How long is the open tube in the slide whistle for this frequency?
See all solutions

Recommended explanations on Physics Textbooks

Physical Quantities And Units

Read Explanation

Electricity and Magnetism

Read Explanation

Astrophysics

Read Explanation

Particle Model of Matter

Read Explanation

Nuclear Physics

Read Explanation

Rotational Dynamics

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.