Physics for Scientists and Engineers
10th Edition
ISBN: 9781337553278
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 17, Problem 22P
Ever since seeing Figure 16.22 in the previous chapter, you have been fascinated with the hearing response in humans. You have set up an apparatus that allows you to determine your own threshold of hearing as a function of frequency. After performing the experiment and recording the results, you graph the results, which look like Figure P17.22. You are intrigued by the two dips in the curve at the right-hand side of the graph. You measure carefully and find that the minimum values of these dips occur at 3 800 Hz and 11 500 Hz. Performing some online research, you discover that the outer canal of the human ear can be modeled as an air column open at the outer end and closed at the inner end by the eardrum. You use this information to determine the length of the outer canal in your car.
Figure P17.22
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Certain species of mice have a threshold of hearing below that of humans.
Suppose you're sitting on a grassy knoll relaxing in the sunlight on a beautiful spring day out in the country. The air is still, and it's quiet. A bird is on the grass about two meters behind you and makes a faint rustling sound in the grass, and the sound is just barely at the threshold of your hearing. At the same time, the mouse whose hearing threshold is −3dB is somewhere nearby, and the rustling sound is also at the threshold of its hearing. How far (in meters) is the mouse from the bird?
(To check your answer, ask yourself if you expected the mouse to be further from or closer to the bird than you. Why?)
Sound is detected when a sound wave causes the eardrum to vibrate (as shown). Typically, the diameter of the eardrum is about 8.4 mm in humans. When someone speaks to you in a normal tone of voice, the sound intensity at your ear is approximately 1.0 × 10-6 W/m2. How much energy is delivered to your eardrum each second?
Item 9
Learning Goal:
To learn the properties of logarithms and how to manipulate them when
solving sound problems.
The intensity of sound is the power of the sound waves divided by the area
on which they are incident. Intensity is measured in watts per square meter,
or W/m².
The human ear can detect a remarkable range of sound intensities. The
quietest sound that we can hear has an intensity of 10-¹2 W/m², and we
begin to feel pain when the intensity reaches 1 W/m². Since the
intensities that matter to people in everyday life cover a range of 12 orders
of magnitude, intensities are usually converted to a logarithmic scale called
the sound intensity level 3, which is measured in decibels (dB). For a given
sound intensity I, B is found from the equation
ß = (10 dB) log (1).
where Io = 1.0 × 10-¹2 W/m².
Part A
What is the value of log(1,000,000)?
Express your answer as an integer.
► View Available Hint(s)
The logarithm of x, written log(x), tells you the power to which you would raise 10…
Chapter 17 Solutions
Physics for Scientists and Engineers
Ch. 17.1 - Prob. 17.1QQCh. 17.2 - Consider the waves in Figure 17.8 to be waves on a...Ch. 17.4 - When a standing wave is set up on a string fixed...Ch. 17.6 - Prob. 17.4QQCh. 17.6 - Balboa Park in San Diego has an outdoor organ....Ch. 17 - Two waves on one string are described by the wave...Ch. 17 - Two pulses of different amplitudes approach each...Ch. 17 - Two wave pulses A and B are moving in opposite...Ch. 17 - Why is the following situation impossible? Two...Ch. 17 - Two pulses traveling on the same string are...
Ch. 17 - Two identical loudspeakers 10.0 m apart are driven...Ch. 17 - Two sinusoidal waves on a string are defined by...Ch. 17 - Verify by direct substitution that the wave...Ch. 17 - Prob. 9PCh. 17 - A standing wave is described by the wave function...Ch. 17 - Prob. 11PCh. 17 - A taut string has a length of 2.60 m and is fixed...Ch. 17 - A string that is 30.0 cm long and has a mass per...Ch. 17 - In the arrangement shown in Figure P17.14, an...Ch. 17 - Review. A sphere of mass M = 1.00 kg is supported...Ch. 17 - Review. A sphere of mass M is supported by a...Ch. 17 - Prob. 17PCh. 17 - Review. A solid copper object hangs at the bottom...Ch. 17 - The Bay of Fundy, Nova Scotia, has the highest...Ch. 17 - Prob. 20PCh. 17 - The fundamental frequency of an open organ pipe...Ch. 17 - Ever since seeing Figure 16.22 in the previous...Ch. 17 - An air column in a glass tube is open at one end...Ch. 17 - A shower stall has dimensions 86.0 cm 86.0 cm ...Ch. 17 - Prob. 25PCh. 17 - Prob. 26PCh. 17 - As shown in Figure P17.27, water is pumped into a...Ch. 17 - As shown in Figure P17.27, water is pumped into a...Ch. 17 - Prob. 29PCh. 17 - Why is the following situation impossible? A...Ch. 17 - Review. A student holds a tuning fork oscillating...Ch. 17 - Prob. 32PCh. 17 - Suppose a flutist plays a 523-Hz C note with first...Ch. 17 - Two strings are vibrating at the same frequency of...Ch. 17 - Prob. 35APCh. 17 - A 2.00-m-long wire having a mass of 0.100 kg is...Ch. 17 - Prob. 37APCh. 17 - You are working as an assistant to a landscape...Ch. 17 - Review. Consider the apparatus shown in Figure...Ch. 17 - Review. For the arrangement shown in Figure...Ch. 17 - Review. A loudspeaker at the front of a room and...Ch. 17 - Two speakers are driven by the same oscillator of...Ch. 17 - A standing wave is set up in a string of variable...Ch. 17 - Review. The top end of a yo-yo string is held...Ch. 17 - Prob. 45APCh. 17 - Prob. 46APCh. 17 - Review. A 12.0-kg object hangs in equilibrium from...Ch. 17 - Review. An object of mass m hangs in equilibrium...Ch. 17 - Two waves are described by the wave functions...Ch. 17 - Prob. 50CP
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- Item 9 Learning Goal: To learn the properties of logarithms and how to manipulate them when solving sound problems. The intensity of sound is the power of the sound waves divided by the area on which they are incident. Intensity is measured in watts per square meter, or W/m². The human ear can detect a remarkable range of sound intensities. The quietest sound that we can hear has an intensity of 10-12 W/m², and we begin to feel pain when the intensity reaches 1 W/m². Since the intensities matter people in everyday life cover a range of 12 orders of magnitude, intensities are usually converted to a logarithmic scale called the sound intensity level 3, which is measured in decibels (dB). For a given sound intensity I, B is found from the equation ß = (10 dB) log (1), where Io = 1.0 × 10-¹2 W/m². ▼ The logarithm of x, written log(x), tells you the power to which you would raise 10 to get æ. So, if y = log(x), then x = 10³. It is easy to take the logarithm of a number such as 10², because…arrow_forwardTwo students hear the same sound and their eardrums receive the same power from the sound wave. The sound intensity at the eardrums of the first student is 0.93 W/m2, while at the eardrums of the second student the sound intensity is 1.16 times greater. If the diameter of the second student’s eardrum is 1.1 cm, how much acoustic power, in microwatts, is striking each of his (and the other student’s) eardrums?arrow_forwardA sound wave with intensity 2 x 10 -3 W/m2 is perceived to be modestly loud. Your eardrum is 6 mm in diameter. How much energy will be transferred to your eardrum while listening to this sound for 1 minute?arrow_forward
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- The decibel scale is useful because A it can be used to represent the very large range of pressure differences that humans hear. B it is a measure of loudness and not stimulus amplitude. C loudness is related only to the frequency of the stimulus. D loudness is related only to the amplitude of the stimulus.arrow_forwardSperm whales, just like bats, use echolocation to find prey. A sperm whale’s vocal system creates a single sharp click, but the emitted sound consists of several equally spaced clicks of decreasing intensity. Researchers use the time interval between the clicks to estimate the size of the whale that created them. Explain how this might be done.arrow_forwardFor Exercise, the formula L = 10 log (£) gives the loudness of sound L (in dB) based on the intensity of sound I (in W/m2). The value 10 = 10-12 W/m2 is the minimal threshold for hearing for midfrequency sounds. Hearing impairment is often measured according to the minimal sound level (in dB) detected by an individual for sounds at various frequencies. For one frequency, the table depicts the level of hearing impairment. Category Loudness (dB) Mild 26 sLs 40 Moderate 41 90 a. If the minimum intensity heard by an individual is 3.4 x 10-8 W/m2, determine if the individual has a hearing impairment. b. If the minimum loudness of sound detected by an individual is 30 dB, determine the corresponding intensity of sound.arrow_forward
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