Physics II Chapter 17: Introduction to the Physics of Hearing

An organ pipe is 112 cm long. What are the fundamental and first three audible overtones if the pipe is: (a) closed at one end, and (b) open at both ends?

(a) if the pipe is closed at one end, only the odd harmonic frequencies are present, and are given by: fn = nv/4L = nf, where n = 1, 3, 5, .... f1 = v/4L = 343 m/s/4*1.12m = 76.6 Hz f3 = 3*f1 = 230 Hz, f5 = 5*f1 = 383 Hz, f7 = 7f1 = 536 Hz (b) if the pipe is open at both ends, all the harmonic frequencies are present, and are given by fn = v/wavelength = nv/2L = nf, where n = 1, 2, 3, .... f1 = v/2L = (343 m/s)/(2 * 1.12m) = 153 Hz f2 = 2*f1 = 306 Hz, f3 = 3*f1 459 Hz, f4 = 4*f1 = 612 Hz

A uniform narrow tube 1.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is (a) the fundamental frequency, and (b) the speed of sound in the gas in the tube?

(a) the difference between successive overtones for an open pipe is the fundamental frequency, f1 = 330 Hz - 275 Hz = 55 Hz (b) the fundamental frequency is given by f1 = v/2*I, Solve this for the speed for sound ----> v = 2I, f1 = 2(1.8m)(55Hz) = 198 m/s = 2.0 x10^2 m/s

The allowed standing-wave frequencies are all integer multiples of the fundamental frequency called harmonies. Equation?

The allowed standing-wave frequencies are all integer multiples of the fundamental frequency called harmonies. Equation? f = n*f where n = 1, 2, 3, 4, ....

The _________________ determine how much it will compress under a given amount of external pressure. The ratio of the change in pressure to the fractional volume compression is called the ______________.

The bulk elastic properties of a material determine how much it will compress under a given amount of external pressure. The ratio of the change in pressure to the fractional volume compression is called the bulk modulus of the material.

What are the units of density?

kg/m^3

log(1) = ? log(10) = ? log (100) = ? log (0.1) = ? log (0.01) = ? log (0.001) = ?

log(1) = 0 log(10) = 1 log (100) = 2 log (0.1) = -1 log (0.01) = -2 log (0.001) = -3

What is the speed of sound in air at sea level?

vsound = 331 m/s * sqrt(Tk/273K)

How do you calculate the speed of a wave?

vsound = wavelength * frequency

10 dB = __ bel

10 dB = 1 bel

A tube closed at one end (some organ pipes) has a displacement node (and pressure antinode) at the closed end. Equation?

A tube closed at one end (some organ pipes) has a displacement node (and pressure antinode) at the closed end. f = v/wavelength = nv/4L, where n= 1, 3, 5, ....

A unit of the perceived loudness of sounds: ____________.

A unit of the perceived loudness of sounds: phon.

Air Columns A tube open at both ends (most wind instruments) has pressure nodes, and therefore _____________, at the ends Equation?

Air Columns A tube open at both ends (most wind instruments) has pressure nodes, and therefore displacement antinodes, at the ends f = nv/2L = nf

At the closed end of a tube, the air will be a __________ and is not free to move. At the open end of a tube, the air will be a ___________ because the air can move freely. Equation?

At the closed end of a tube, the air will be a displacement node and is not free to move. At the open end of a tube, the air will be a displacement antinode because the air can move freely. f = v/wavelength = nv/4L, where n = 1, 3, 5, .....

Displacement node = ______

Displacement node = pressure antinode

Sound can travel through a vacuum. T or F? Explain.

False. Sound can travel through any kind of material. Sound cannot travel through a vacuum since it needs a source of sound (In Previous Card)

For a string fixed at both ends, the simplest standing wave, the fundamental or first harmonic, has nodes at _________ and an antinode in the ________. The wave speed is determined by the tension in the string and the mass per unit length of the string (linear density, μ). Show the equation.

For a string fixed at both ends, the simplest standing wave, the fundamental or first harmonic, has nodes at both ends and an antinode in the middle. The wave speed is determined by the tension in the string and the mass per unit length of the string (linear density, μ). v = sqrt(T/(m/L)) = sqrt(T/μ)

For an instrument, a standing wave is produced at its resonant frequency.

For an instrument, a standing wave is produced at its ______________.

For fn = nv/2L - first harmonic = _______, __________

For fn = nv/2L - first harmonic = 1/2 * wavelength, open at both ends

For fn = nv/4L - first harmonic = ___________, closed at ________

For fn = nv/4L - first harmonic = 1/4*wavelength, closed at one end

Frequencies of standing-wave nodes of a string of length L (resonant modes or resonant frequencies):

Frequencies of standing-wave nodes of a string of length L(resonant modes or resonant frequencies): fn = v/wavelength = nv/2L where n = 1, 2, 3, ....

Humans can hear sounds with frequencies between ____________. Frequencies above 20,000 Hz are called ___________. Frequencies below 20 Hz are called __________.

Humans can hear sounds with frequencies between 20 and 20,000 Hz (audible range). Frequencies above 20,000 Hz are called ultrasonic. Frequencies below 20 Hz are called infrasonic.

You stand a certain distance away from a speaker and you hear a certain intensity of sound. If you double your distance from the speaker, what happens to the sound intensity at your new position?

I = P/A = pi*r^2 I ∞ 1/r^2 x2 the distance, 1/4 the original value

In air, the speed of sound increases approx. _______ for each C degree increase in temperature. What is the equation?

In air, the speed of sound increases approx. 0.60 m/s for each C degree increase in temperature. v = 331.4 + 0.60 * Tc

Intensity is proportional to the ____________. Show the equation.

Intensity is proportional to the square of the ampitude. I = Power/Area I = deltap^2/2p*v

A guitar string has a mass of 4 g, a length of 74 cm, and a tension of 400 N. a) wave speed = ? b) fundamental frequency = ? c) frequency of the second harmonic = ?

L = 74 cm = 0.74 m v = 274 m/s [v = sqrt(T/(m/L))] wavelength = 2L f = 274/1.48 = 185 Hz 2nd wavelength = L = 370 Hz

Light is a ____________. All ___________ are these kinds of waves.

Light is a transverse wave. All electromagnetic waves are transverse waves.

Longitudinal waves are often called ___________. The displacement is 90 degrees out of phase with the pressure.

Longitudinal waves are often called pressure waves. The displacement is 90 degrees out of phase with the pressure.

___________ is related to the intensity of sound. It is the sensation in the consciousness of a human. Related to the physically measurable quantity of intensity of a wave. _________ is related to frequency; refers to whether the sound is high or low. _________: unit used to measure the intensity of sound.

Loudness is related to the intensity of sound. Pitch is related to frequency; refers to whether the sound is high or low. decibel (dB): unit used to measure the intensity of sound.

Do you expect an echo to return to you more quickly or less quickly on a hot day, as compared to a cold day?

More quickly on a hot day, since the speed of sound in a gas increases with temperature. Speed of sound in air at sea level = 331 * sqrt(Tk/273K)

Outer ear: ______________ Middle ear: ____________ Inner ear: _____________

Outer ear: sound waves travel down the ear canal to the eardrum, which vibrates in response Middle ear: hammer, anvil, and stirrup transfer vibrations to inner ear Inner ear: cochlea transforms vibrational energy to electrical energy and sends signals to the brain

Second harmonic = ______ overtone Third harmonic = ______ overtone

Second harmonic = first overtone Third harmonic = second overtone

Sound waves interfere in the same way that other waves do in space. When two waves simultaneously pass through the same regions of space, they interfere with each other. Waves can also interfere in time, causing a phenomenon called _______. Beats are the slow "envelope" around two waves that are relatively close in frequency. The beat frequency is equal to the absolute value of the difference in frequency of the two waves. Equation?

Sound waves interfere in the same way that other waves do in space. When two waves simultaneously pass through the same regions of space, they interfere with each other. Waves can also interfere in time, causing a phenomenon called beats. Beats are the slow "envelope" around two waves that are relatively close in frequency. The beat frequency is equal to the absolute value of the difference in frequency of the two waves. fbeat = |f1 - f2|

The ear is __________ to all frequencies. To hear the same loudness for sounds of different frequencies requires different intensities.

The ear is not equally sensitive to all frequencies. To hear the same loudness for sounds of different frequencies requires different intensities.

If you fill your lungs with helium and then try talking, you sound like Donald Duck. What conclusion can you reach about the speed of sound in helium?

The higher pitch implies a higher frequency. In turn, since v = frequency * wavelength, this means that the speed of the wave has increased (as long as the wavelength, det. by the length of the vocal chords, remains constant). Therefore, the speed of sound is greater in helium.

The intensity of wave is the ______________. The human ear can detect sounds with an intensity as low as ________ and as high as ________.

The intensity of wave is the energy transported per unit time across a unit area. The human ear can detect sounds with an intensity as low as 10^-12 W/m^2 and as high as 1 W/m^2.

The loudness of a sound is much more closely related to the logarithm of the intensity. Sound level is defined as __________, where I0 = _____

The loudness of a sound is much more closely related to the logarithm of the intensity. Sound level is defined as B = 10log(I/I0), where I0 = 1.0 x 10^-12 W/m^2

The pitch of a string of a given length can be altered by using a string of __________. Also by changing the ________ - the strings on a guitar can be effectively shortened by placing the finger on the string of a guitar, raising the fundamental pitch. A piano uses both methods to cover its more than 7-octave range - the lower strings are longer and thicker than the higher ones.

The pitch of a string of a given length can be altered by using a string of different density. Also by changing the length - the strings on a guitar can be effectively shortened by placing the finger on the string of a guitar, raising the fundamental pitch. A piano uses both methods to cover its more than 7-octave range - the lower strings are longer and thicker than the higher ones.

The speed of sound for a uniform medium is determined by its ___________ and its _______. Show the equation.

The speed of sound for a uniform medium is determined by its elastic property (bulk modulus) and its density. v = sqrt(B/p)

The speed of sound in a gas increases with ___________.

The speed of sound in a gas increases with temperature.

The speed of sound is slowest in _______, faster in ________, and fastest in ______.

The speed of sound is slowest in gases, faster in liquids, and fastest in solids.

The threshold of hearing is the _________ to a good ear.

The threshold of hearing is the min. intensity audible to a good ear.

The transverse waves on a vibrating string are different from sound waves. T or F? Explain.

True. For transverse waves, the displacement of the medium is perpendicular to the direction of the propagation of the wave. May occur on a string, on the surface of a liquid, and throughout a solid. Transverse waves cannot propagate in a gas or a liquid because there is no mechanism for driving motion perpendicular to the propagation of the wave.

Light travels much faster than sound. T or F? Explain.

True. Light does not need a medium to travel. Speed of light is 3 x 10^8 m/s. Speed of sound is 340 m/s.

Sound waves are longitudinal pressure waves. T or F? Explain.

True. Sound is a longitudinal wave. There must be a source for sound (aka a vibrating object; medium). The energy is transferred from the source in the form of longitudinal sound waves. The sound is detected by an ear or an instrument. Hearing is the perception of sound.

"Pitch" (in music) and frequency have approx. the same meaning. T or F? Explain.

True. They are not equivalent however. Frequency is an objective attribute that can be measured. Pitch is each person's subjective perception of a sound wave. Frequency measures the cycle rate of the physical waveform, pitch is how high or low is sounds when you hear it.

Why does a trumpet sound different from a flute? The answer lies in _________ -- which ones are present, and how strong they are, makes a big difference.

Why does a trumpet sound different from a flute? The answer lies in overtones -- which ones are present, and how strong they are, makes a big difference.

Wind instruments create sound through ________ in a column of air.

Wind instruments create sound through standing waves in a column of air.

Does a longitudinal wave, such as a sound wave, have an amplitude?

Yes. The amplitude of a wave is the max. displacement from equilibrium. For a longitudinal wave, which is a pressure wave, this would be the maximum increase (or decrease) in pressure from the equilibrium pressure that is caused when a compression (or rarefaction) passes a point. The amplitude is the distance from the equilibrium position of the medium to a compression or a rarefaction.

Fundamental frequency equation

f1 = v/wavelength = v/2L

x = log*y = ?

y = 10^x