Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 16: Problem 48

A bugle can be represented by a cylindrical pipe of length \(L=1.35 \mathrm{~m} .\) Since the ends are open, the standing waves produced in the bugle have antinodes at the open ends, where the air molecules move back and forth the most. Calculate the longest three wavelengths of standing waves inside the bugle. Also calculate the three lowest frequencies and the three longest wavelengths of the sound that is produced in the air around the bugle.

Short Answer

Expert verified
Answer: The three longest wavelengths inside the bugle are 2.70 meters, 1.35 meters, and 0.90 meters. The three lowest frequencies are approximately 127.04 Hz, 254.07 Hz, and 381.11 Hz. The three longest wavelengths of the sound produced in the air around the bugle are also 2.70 meters, 1.35 meters, and 0.90 meters.

Step by step solution

01

Understand the characteristics of open pipes

In an open pipe, both ends have antinodes. The simplest standing wave can be created, when we have only one antinode more than the endpoints, which is half a wavelength (λ/2). In the case of open pipes, the fundamental frequency or first harmonic has a length of L = λ/2. For higher harmonics, the length is given by L = n(λ/2), where n is the harmonic number.
02

Calculate the three longest wavelengths inside the bugle

Let's find the longest three wavelengths inside the bugle by using the formula L = n(λ/2), and solve for λ. We will do this for n = 1, 2, and 3, as they represent the three lowest harmonics. λ1 = 2 * L / 1 λ2 = 2 * L / 2 λ3 = 2 * L / 3 Plug in the given length, L = 1.35 meters: λ1 = 2 * 1.35 / 1 λ1 = 2.70 meters λ2 = 2 * 1.35 / 2 λ2 = 1.35 meters λ3 = 2 * 1.35 / 3 λ3 = 0.90 meters The three longest wavelengths inside the bugle are 2.70 meters, 1.35 meters, and 0.90 meters.
03

Calculate the three lowest frequencies

Now, let's find the three lowest frequencies of standing waves inside the bugle. We will use the equation f = v / λ, where f is the frequency, v is the speed of sound (approximately 343 meters/second for air), and λ is the wavelength. f1 = v / λ1 f2 = v / λ2 f3 = v / λ3 Use speed of sound in air, v = 343 meters/second: f1 = 343 / 2.70 f1 ≈ 127.04 Hz f2 = 343 / 1.35 f2 ≈ 254.07 Hz f3 = 343 / 0.90 f3 ≈ 381.11 Hz The three lowest frequencies are approximately 127.04 Hz, 254.07 Hz, and 381.11 Hz.
04

Calculate the wavelengths of the sound produced in the air around the bugle

The wavelengths of the sound produced in the air around the bugle are the same as the wavelengths inside the bugle. Therefore, the three longest wavelengths of the sound produced in the air around the bugle are 2.70 meters, 1.35 meters, and 0.90 meters.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

A standing wave in a pipe with both ends open has a frequency of \(440 \mathrm{~Hz}\). The next higher harmonic has a frequency of \(660 \mathrm{~Hz}\) a) Determine the fundamental frequency. b) How long is the pipe?

A sound meter placed \(3 \mathrm{~m}\) from a speaker registers a sound level of \(80 \mathrm{~dB}\). If the volume on the speaker is then turned down so that the power is reduced by a factor of 25 , what will the sound meter read? a) \(3.2 \mathrm{~dB}\) c) \(32 \mathrm{~dB}\) e) \(66 \mathrm{~dB}\) b) \(11 \mathrm{~dB}\) d) \(55 \mathrm{~dB}\)

You are traveling in a car toward a hill at a speed of \(40.0 \mathrm{mph} .\) The car's horn emits sound waves of frequency \(250 \mathrm{~Hz},\) which move with a speed of \(340 \mathrm{~m} / \mathrm{s}\) a) Determine the frequency with which the waves strike the hill. b) What is the frequency of the reflected sound waves you hear? c) What is the beat frequency produced by the direct and the reflected sounds at your ears?

Two trains are traveling toward each other in still air at \(25.0 \mathrm{~m} / \mathrm{s}\) relative to the ground. One train is blowing a whistle at \(300 .\) Hz. The speed of sound is \(343 \mathrm{~m} / \mathrm{s}\). a) What frequency is heard by a man on the ground facing the whistle-blowing train? b) What frequency is heard by a man on the other train?

A string of a violin produces 2 beats per second when sounded along with a standard fork of frequency \(400 . \mathrm{Hz}\). The beat frequency increases when the string is tightened. a) What was the frequency of the violin at first? b) What should be done to tune the violin?
See all solutions

Recommended explanations on Physics Textbooks

Linear Momentum

Read Explanation

Space Physics

Read Explanation

Measurements

Read Explanation

Astrophysics

Read Explanation

Medical Physics

Read Explanation

Fluids

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.

Sign-up for free