Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 12: Problem 59

At what frequency \(f\) does a sound wave in air have a wavelength of $15 \mathrm{cm},$ about half the diameter of the human head? Some methods of localization work well only for frequencies below \(f\), while others work well only above \(f\). (See Conceptual Questions 4 and 5 .)

Short Answer

Expert verified
Answer: The frequency of the sound wave is approximately 2287 Hz.

Step by step solution

01

Convert wavelength to meters

Since the given wavelength is 15 cm, we need to convert it to meters: \(\lambda = 15 \mathrm{cm} = 0.15 \,\mathrm{m}\). This will allow us to use the wavelength in the formula with the correct units.
02

Find the velocity of sound in air

The velocity of sound in air, at room temperature (20°C), is approximately 343 m/s. Keep in mind that the velocity of sound depends on the temperature.
03

Use the formula to find the frequency

We know the velocity of sound in air, \(v=343 \, \mathrm{m/s}\), and the wavelength, \(\lambda = 0.15 \, \mathrm{m}\). We will plug in these values into the formula \(v = f\lambda\) and solve for \(f\): $$ f = \frac{v}{\lambda} = \frac{343 \, \mathrm{m/s}}{0.15 \, \mathrm{m}} \approx 2287 \, \mathrm{Hz} $$
04

Interpret the result

The sound wave in air has a frequency of approximately 2287 Hz when its wavelength is 15 cm (0.15 m). Some methods of localization work well only for frequencies below 2287 Hz, while others work well only above 2287 Hz.

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

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?
A geological survey ship mapping the floor of the ocean sends sound pulses down from the surface and measures the time taken for the echo to return. How deep is the ocean at a point where the echo time (down and back) is $7.07 \mathrm{s} ?\( The temperature of the seawater is \)25^{\circ} \mathrm{C}$
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.
Doppler ultrasound is used to measure the speed of blood flow (see Problem 42). The reflected sound interferes with the emitted sound, producing beats. If the speed of red blood cells is \(0.10 \mathrm{m} / \mathrm{s},\) the ultrasound frequency used is \(5.0 \mathrm{MHz},\) and the speed of sound in blood is \(1570 \mathrm{m} / \mathrm{s},\) what is the beat frequency?
An auditorium has organ pipes at the front and at the rear of the hall. Two identical pipes, one at the front and one at the back, have fundamental frequencies of \(264.0 \mathrm{Hz}\) at \(20.0^{\circ} \mathrm{C} .\) During a performance, the organ pipes at the back of the hall are at $25.0^{\circ} \mathrm{C},\( while those at the front are still at \)20.0^{\circ} \mathrm{C} .$ What is the beat frequency when the two pipes sound simultaneously?
See all solutions

Recommended explanations on Physics Textbooks

Fundamentals of Physics

Read Explanation

Space Physics

Read Explanation

Wave Optics

Read Explanation

Waves Physics

Read Explanation

Atoms and Radioactivity

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