Skip to main content
Ch 15: Mechanical Waves
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 15th EditionCh 15: Mechanical WavesProblem 25
Chapter 15, Problem 25

A jet plane at takeoff can produce sound of intensity 10.0 W/m2 at 30.0 m away. But you prefer the tranquil sound of normal conversation, which is 1.0 μW/m2. Assume that the plane behaves like a point source of sound. (a) What is the closest dis-tance you should live from the airport runway to preserve your peace of mind? (b) What intensity from the jet does your friend experience if she lives twice as far from the runway as you do? (c) What power of sound does the jet produce at takeoff?

Verified step by step guidance
1
Step 1: Understand the concept of sound intensity and how it relates to distance from a point source. The intensity of sound from a point source decreases with the square of the distance from the source. This is known as the inverse square law for sound intensity.
Step 2: Use the inverse square law to find the closest distance you should live from the airport runway. The formula for sound intensity is I = P / (4πr²), where I is the intensity, P is the power of the source, and r is the distance from the source. You need to solve for r when I is 1.0 μW/m².
Step 3: Calculate the intensity your friend experiences if she lives twice as far from the runway as you do. Use the inverse square law again, knowing that if the distance is doubled, the intensity will be reduced by a factor of four.
Step 4: Determine the power of sound the jet produces at takeoff. Use the given intensity at 30.0 m (10.0 W/m²) and the formula I = P / (4πr²) to solve for P, the power of the sound source.
Step 5: Review the calculations and ensure that the units are consistent throughout the problem. Make sure to convert units where necessary, such as converting μW to W for consistency in calculations.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
8m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Sound Intensity

Sound intensity is the power per unit area carried by a sound wave, measured in watts per square meter (W/m^2). It quantifies how much sound energy passes through a given area and is crucial for understanding the loudness of sound at different distances from the source.
Recommended video:
Guided course
04:25
Sound Intensity Level and the Decibel Scale

Inverse Square Law

The inverse square law states that the intensity of sound from a point source decreases with the square of the distance from the source. This means that as you move away from the sound source, the intensity diminishes rapidly, which is essential for calculating sound levels at various distances.
Recommended video:
Guided course
05:26
The Inverse-Square Law for Intensity

Sound Power

Sound power is the total energy emitted by a sound source per unit time, measured in watts (W). Unlike intensity, sound power is independent of distance and describes the source's ability to produce sound, which is vital for determining the total acoustic output of the jet plane.
Recommended video:
Guided course
04:25
Sound Intensity Level and the Decibel Scale
Related Practice
Textbook Question

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x,t)=(2.30mm)cos[(16.98 rad/m)x+(742 rad/s)t]y(x,t)=\(\left\)(2.30\(\operatorname{mm)}\]\cos\)[\(\left\)(16.98\(\text{ }\)rad/m\(\right\))x+(742\(\text{ }\)rad/s\(\right\))t]. Being more practical, you measure the rope to have a length of 1.35 m1.35\(\text{ m}\) and a mass of 0.00338kg0.00338\(\operatorname{kg}\). You are then asked to determine the following: (f) tension in the rope; (g) average power transmitted by the wave.

1
views
Textbook Question

Threshold of Pain. You are investigating the report of a UFO landing in an isolated portion of New Mexico, and you encounter a strange object that is radiating sound waves uniformly in all directions. Assume that the sound comes from a point source and that you can ignore reflections. You are slowly walking toward the source. When you are 7.5 m from it, you measure its intensity to be 0.11 W/m2. An intensity of 1.0 W/m2 is often used as the 'threshold of pain.' How much closer to the source can you move before the sound intensity reaches this threshold?

1
views
Textbook Question

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x,t)=(2.30mm)cos[(16.98 rad/m)x+(742 rad/s)t]y(x,t)=\(\left\)(2.30\(\operatorname{mm)}\]\cos\)[\(\left\)(16.98\(\text{ }\)rad/m\(\right\))x+(742\(\text{ }\)rad/s\(\right\))t]. Being more practical, you measure the rope to have a length of 1.35 m1.35\(\text{ m}\) and a mass of 0.00338kg0.00338\(\operatorname{kg}\). You are then asked to determine the following: (d) wave speed; (e) direction the wave is traveling;

1
views
Textbook Question

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x,t)=(2.30mm)cos[(16.98 rad/m)x+(742 rad/s)t]y(x,t)=\(\left\)(2.30\(\operatorname{mm)}\]\cos\)[\(\left\)(16.98\(\text{ }\)rad/m\(\right\))x+(742\(\text{ }\)rad/s\(\right\))t]. Being more practical, you measure the rope to have a length of 1.35 m1.35\(\text{ m}\) and a mass of 0.00338kg0.00338\(\operatorname{kg}\). You are then asked to determine the following: (a) amplitude; (b) frequency; (c) wavelength.

1
views
Textbook Question

The speed of sound in air at 20°C is 344 m/s. (a) What is the wavelength of a sound wave with a frequency of 784 Hz, corresponding to the note G5 on a piano, and how many milliseconds does each vibration take? (b) What is the wavelength of a sound wave one octave higher (twice the frequency) than the note in part (a)?

2
views