Chapter 17: Physics of HearingContent check — College Physics (AP), Chapter 17: Physics of Hearing

When poked by a spear, an operatic soprano lets out a 1200-Hz shriek. What is its wavelength if the speed of sound is 345 m/s?

Calculate the speed of sound on a day when a 1500 Hz frequency has a wavelength of 0.221 m.

Show that the speed of sound in $\text{20.0ºC}$ air is 343 m/s, as claimed in the text.

Dolphins make sounds in air and water. What is the ratio of the wavelength of a sound in air to its wavelength in seawater? Assume air temperature is $\text{20.0ºC}$.

(a) If a submarine’s sonar can measure echo times with a precision of 0.0100 s, what is the smallest difference in distances it can detect? (Assume that the submarine is in the ocean, not in fresh water.)

(b) Discuss the limits this time resolution imposes on the ability of the sonar system to detect the size and shape of the object creating the echo.

Suppose a bat uses sound echoes to locate its insect prey, 3.00 m away. (See Figure 17.9.) (a) Calculate the echo times for temperatures of $\text{5.00ºC}$ and $\text{35.0ºC}$. (b) What percent uncertainty does this cause for the bat in locating the insect? (c) Discuss the significance of this uncertainty and whether it could cause difficulties for the bat. (In practice, the bat continues to use sound as it closes in, eliminating most of any difficulties imposed by this and other effects, such as motion of the prey.)

What is the intensity in watts per meter squared of 85.0-dB sound?

A sound wave traveling in $\mathrm{20ºC}$ air has a pressure amplitude of 0.5 Pa. What is the intensity of the wave?

What sound intensity level in dB is produced by earphones that create an intensity of $4.00\times {\text{10}}^{\text{−2}}{\text{W/m}}^{\text{2}}$?

(a) What is the decibel level of a sound that is twice as intense as a 90.0-dB sound? (b) What is the decibel level of a sound that is one-fifth as intense as a 90.0-dB sound?

(a) How much more intense is a sound that has a level 17.0 dB higher than another? (b) If one sound has a level 23.0 dB less than another, what is the ratio of their intensities?

If a large housefly 3.0 m away from you makes a noise of 40.0 dB, what is the noise level of 1000 flies at that distance, assuming interference has a negligible effect?

The amplitude of a sound wave is measured in terms of its maximum gauge pressure. By what factor does the amplitude of a sound wave increase if the sound intensity level goes up by 40.0 dB?

An 8-hour exposure to a sound intensity level of 90.0 dB may cause hearing damage. What energy in joules falls on a 0.800-cm-diameter eardrum so exposed?

Sound is more effectively transmitted into a stethoscope by direct contact than through the air, and it is further intensified by being concentrated on the smaller area of the eardrum. It is reasonable to assume that sound is transmitted into a stethoscope 100 times as effectively compared with transmission though the air. What, then, is the gain in decibels produced by a stethoscope that has a sound gathering area of ${\mathrm{15.0\; cm}}^2$, and concentrates the sound onto two eardrums with a total area of ${\mathrm{0.900\; cm}}^2$ with an efficiency of 40.0%?

(a) What frequency is received by a person watching an oncoming ambulance moving at 110 km/h and emitting a steady 800-Hz sound from its siren? The speed of sound on this day is 345 m/s. (b) What frequency does she receive after the ambulance has passed?

What frequency is received by a mouse just before being dispatched by a hawk flying at it at 25.0 m/s and emitting a screech of frequency 3500 Hz? Take the speed of sound to be 331 m/s.

A commuter train blows its 200-Hz horn as it approaches a crossing. The speed of sound is 335 m/s. (a) An observer waiting at the crossing receives a frequency of 208 Hz. What is the speed of the train? (b) What frequency does the observer receive as the train moves away?

Two eagles fly directly toward one another, the first at 15.0 m/s and the second at 20.0 m/s. Both screech, the first one emitting a frequency of 3200 Hz and the second one emitting a frequency of 3800 Hz. What frequencies do they receive if the speed of sound is 330 m/s?

A “showy” custom-built car has two brass horns that are supposed to produce the same frequency but actually emit 263.8 and 264.5 Hz. What beat frequency is produced?

What beat frequencies result if a piano hammer hits three strings that emit frequencies of 127.8, 128.1, and 128.3 Hz?

(a) What is the fundamental frequency of a 0.672-m-long tube, open at both ends, on a day when the speed of sound is 344 m/s? (b) What is the frequency of its second harmonic?

What are the first three overtones of a bassoon that has a fundamental frequency of 90.0 Hz? It is open at both ends. (The overtones of a real bassoon are more complex than this example, because its double reed makes it act more like a tube closed at one end.)

What length should an oboe have to produce a fundamental frequency of 110 Hz on a day when the speed of sound is 343 m/s? It is open at both ends.

(a) Find the length of an organ pipe closed at one end that produces a fundamental frequency of 256 Hz when air temperature is $\mathrm{18.0ºC}$. (b) What is its fundamental frequency at $\mathrm{25.0ºC}$?

The ear canal resonates like a tube closed at one end. (See Figure 17.37.) If ear canals range in length from 1.80 to 2.60 cm in an average population, what is the range of fundamental resonant frequencies? Take air temperature to be $\mathrm{37.0ºC}$, which is the same as body temperature. How does this result correlate with the intensity versus frequency graph (Figure 17.35 of the human ear?

A crude approximation of voice production is to consider the breathing passages and mouth to be a resonating tube closed at one end. (See Figure 17.29.) (a) What is the fundamental frequency if the tube is 0.240-m long, by taking air temperature to be $\mathrm{37.0ºC}$? (b) What would this frequency become if the person replaced the air with helium? Assume the same temperature dependence for helium as for air.

What frequencies will a 1.80-m-long tube produce in the audible range at $\mathrm{20.0ºC}$ if: (a) The tube is closed at one end? (b) It is open at both ends?

The factor of ${\text{10}}^{-\text{12}}$ in the range of intensities to which the ear can respond, from threshold to that causing damage after brief exposure, is truly remarkable. If you could measure distances over the same range with a single instrument and the smallest distance you could measure was 1 mm, what would the largest be?

What are the closest frequencies to 500 Hz that an average person can clearly distinguish as being different in frequency from 500 Hz? The sounds are not present simultaneously.

If your radio is producing an average sound intensity level of 85 dB, what is the next lowest sound intensity level that is clearly less intense?

Based on the graph in Figure 17.34, what is the threshold of hearing in decibels for frequencies of 60, 400, 1000, 4000, and 15,000 Hz? Note that many AC electrical appliances produce 60 Hz, music is commonly 400 Hz, a reference frequency is 1000 Hz, your maximum sensitivity is near 4000 Hz, and many older TVs produce a 15,750 Hz whine.

What is the approximate sound intensity level in decibels of a 600-Hz tone if it has a loudness of 20 phons? If it has a loudness of 70 phons?

Suppose a person has a 50-dB hearing loss at all frequencies. By how many factors of 10 will low-intensity sounds need to be amplified to seem normal to this person? Note that smaller amplification is appropriate for more intense sounds to avoid further hearing damage.

(a) What is the intensity in watts per meter squared of a just barely audible 200-Hz sound? (b) What is the intensity in watts per meter squared of a barely audible 4000-Hz sound?

A person has a hearing threshold 10 dB above normal at 100 Hz and 50 dB above normal at 4000 Hz. How much more intense must a 100-Hz tone be than a 4000-Hz tone if they are both barely audible to this person?

What is the ratio of intensities of two sounds of identical frequency if the first is just barely discernible as louder to a person than the second?

Unless otherwise indicated, for problems in this section, assume that the speed of sound through human tissues is 1540 m/s.

What is the sound intensity level in decibels of ultrasound of intensity ${\text{10}}^5{\text{W/m}}^2$, used to pulverize tissue during surgery?

Unless otherwise indicated, for problems in this section, assume that the speed of sound through human tissues is 1540 m/s.

Find the sound intensity level in decibels of $2.00\times {\text{10}}^{\mathrm{–2}}{\text{W/m}}^2$ultrasound used in medical diagnostics.

Unless otherwise indicated, for problems in this section, assume that the speed of sound through human tissues is 1540 m/s.

In the clinical use of ultrasound, transducers are always coupled to the skin by a thin layer of gel or oil, replacing the air that would otherwise exist between the transducer and the skin. (a) Using the values of acoustic impedance given in Table 17.5 calculate the intensity reflection coefficient between transducer material and air. (b) Calculate the intensity reflection coefficient between transducer material and gel (assuming for this problem that its acoustic impedance is identical to that of water). (c) Based on the results of your calculations, explain why the gel is used.

Unless otherwise indicated, for problems in this section, assume that the speed of sound through human tissues is 1540 m/s.

(a) Find the size of the smallest detail observable in human tissue with 20.0-MHz ultrasound. (b) Is its effective penetration depth great enough to examine the entire eye (about 3.00 cm is needed)? (c) What is the wavelength of such ultrasound in $\mathrm{0ºC}$ air?

Unless otherwise indicated, for problems in this section, assume that the speed of sound through human tissues is 1540 m/s.

(a) How far apart are two layers of tissue that produce echoes having round-trip times (used to measure distances) that differ by $\mathrm{0.750\; \mu s}$ ? (b) What minimum frequency must the ultrasound have to see detail this small?

Unless otherwise indicated, for problems in this section, assume that the speed of sound through human tissues is 1540 m/s.

A dolphin is able to tell in the dark that the ultrasound echoes received from two sharks come from two different objects only if the sharks are separated by 3.50 m, one being that much farther away than the other. (a) If the ultrasound has a frequency of 100 kHz, show this ability is not limited by its wavelength. (b) If this ability is due to the dolphin’s ability to detect the arrival times of echoes, what is the minimum time difference the dolphin can perceive?

Unless otherwise indicated, for problems in this section, assume that the speed of sound through human tissues is 1540 m/s.

Ultrasound reflected from an oncoming bloodstream that is moving at 30.0 cm/s is mixed with the original frequency of 2.50 MHz to produce beats. What is the beat frequency? (Assume that the frequency of 2.50 MHz is accurate to seven significant figures.)

A teacher wants to demonstrate that the speed of sound is not a constant value. Considering her regular classroom voice as the control, which of the following will increase the speed of sound leaving her mouth?

I. Submerge her mouth underwater and speak at the same volume.

II. Increase the temperature of the room and speak at the same volume.

III. Increase the pitch of her voice and speak at the same volume.

In order to waken a sleeping child, the volume on an alarm clock is tripled. Under this new scenario, how much more energy will be striking the child’s ear drums each second?

A baggage handler stands on the edge of a runway as a landing plane approaches. Compared to the pitch of the plane as heard by the plane’s pilot, which of the following correctly describes the sensation experienced by the handler?

A common misconception is that two wave pulses traveling in opposite directions will reflect off each other. Outline a procedure that you would use to convince someone that the two wave pulses do not reflect off each other, but instead travel through each other. You may use sketches to represent your understanding. Be sure to provide evidence to not only refute the original claim, but to support yours as well.

A student sends a transverse wave pulse of amplitude A along a rope attached at one end. As the pulse returns to the student, a second pulse of amplitude 3A is sent along the opposite side of the rope. What is the resulting amplitude when the two pulses interact?

A student is shaking a flexible string attached to a wooden board in a rhythmic manner. Which of the following choices will decrease the wavelength within the rope?

I. The student could shake her hand back and forth with greater frequency.

II. The student could shake her hand back in forth with a greater amplitude.

III. The student could increase the tension within the rope by stepping backwards from the board.

A string is vibrating between two posts as shown above. Students are to determine the speed of the wave within this string. They have already measured the amount of time necessary for the wave to oscillate up and down. The students must also take what other measurements to determine the speed of the wave?

A tube is open at one end. If the fundamental frequency f is created by a wavelength λ, then which of the following describes the frequency and wavelength associated with the tube’s fourth overtone?

	f	λ
(a)	4f	λ/4
(b)	4f	λ
(c)	9f	λ/9
(d)	9f	λ

When a student blows across a glass half-full of water, a resonant frequency is created within the air column remaining in the glass. Which of the following can the student do to increase this resonant frequency?

I. Add more water to the glass.

II. Replace the water with a more dense fluid.

III. Increase the temperature of the room.

A student decides to test the speed of sound through wood using a wooden ruler. The student rests the ruler on a desk with half of its length protruding off the desk edge. The student then holds one end in place and strikes the protruding end with his other hand, creating a musical sound, and counts the number of vibrations of the ruler. Explain why the student would not be able to measure the speed of sound through wood using this method.

A musician stands outside in a field and plucks a string on an acoustic guitar. Standing waves will most likely occur in which of the following media? Select two answers.

A student connects one end of a string with negligible mass to an oscillator. The other end of the string is passed over a pulley and attached to a suspended weight, as shown above. The student finds that a standing wave with one antinode is formed on the string when the frequency of the oscillator is f₀. The student then moves the oscillator to shorten the horizontal segment of string to half its original length. At what frequency will a standing wave with one antinode now be formed on the string?