Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 19

Humans can hear sounds with frequencies up to about \(20.0 \mathrm{kHz},\) but dogs can hear frequencies up to about \(40.0 \mathrm{kHz} .\) Dog whistles are made to emit sounds that dogs can hear but humans cannot. If the part of a dog whistle that actually produces the high frequency is made of a tube open at both ends, what is the longest possible length for the tube?

Short Answer

Expert verified
Answer: The longest possible length of the tube is approximately 4.3 mm.

Step by step solution

01

Write down the formula for the fundamental frequency of a tube open at both ends

The formula for the fundamental frequency (\(f_1\)) of a tube open at both ends is: \[f_1 = \frac{v}{2L}\] where: - \(f_1\) is the fundamental frequency, - \(v\) is the speed of sound, - \(L\) is the length of the tube.
02

Substitute the maximum frequency a dog can hear for the fundamental frequency

The maximum frequency a dog can hear is \(40.0 \mathrm{kHz}\). Substitute this value for \(f_1\) in the formula: \[\frac{v}{2L} = 40,000 \,\text{Hz}\]
03

Find the speed of sound in the air

To solve the equation for the length of the tube, we need to know the speed of sound in the air. Consider the speed of sound in air at room temperature (\(20^\circ C\)) to be \(v = 343 \,\text{m/s}\).
04

Solve the equation for the length of the tube

Now substitute the speed of sound into the equation and solve for the length of the tube: \[\frac{343}{2L} = 40,000\] First, multiply both sides of the equation by 2: \[343 = 80,000L\] Now, divide both sides by 80,000: \[L = \frac{343}{80,000} \,\text{m}\]
05

Calculate the longest possible length of the tube

Finally, calculate the value of \(L\): \[L = \frac{343}{80,000} = 0.0042875 \,\text{m}\] The longest possible length for the tube that can produce a frequency only dogs can hear is approximately \(0.0043 \,\text{m}\) or \(4.3 \,\text{mm}\).

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

Bats emit ultrasonic waves with a frequency as high as $1.0 \times 10^{5} \mathrm{Hz} .$ What is the wavelength of such a wave in air of temperature \(15^{\circ} \mathrm{C} ?\)
The Vespertilionidae family of bats detect the distance to an object by timing how long it takes for an emitted signal to reflect off the object and return. Typically they emit sound pulses 3 ms long and 70 ms apart while cruising. (a) If an echo is heard 60 ms later $\left(v_{\text {sound }}=331 \mathrm{m} / \mathrm{s}\right),\( how far away is the object? (b) When an object is only \)30 \mathrm{cm}$ away, how long will it be before the echo is heard? (c) Will the bat be able to detect this echo?
Derive Eq. \((12-4)\) as: (a) Starting with Eq. \((12-3),\) substitute \(T=T_{\mathrm{C}}+273.15 .\) (b) Apply the binomial approximation to the square root (see Appendix A.5) and simplify.
A lightning flash is seen in the sky and 8.2 s later the boom of the thunder is heard. The temperature of the air is \(12^{\circ} \mathrm{C}\) (a) What is the speed of sound at that temperature? [Hint: Light is an electromagnetic wave that travels at a speed of $3.00 \times 10^{8} \mathrm{m} / \mathrm{s} .1$ (b) How far away is the lightning strike?
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

Wave Optics

Read Explanation

Torque and Rotational Motion

Read Explanation

Waves Physics

Read Explanation

Dynamics

Read Explanation

Engineering Physics

Read Explanation

Radiation

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