How to Read Sound Pressure Vs Time Graph

Section Learning Objectives

By the finish of this department, you lot will be able to do the post-obit:

• Chronicle amplitude of a wave to loudness and free energy of a sound wave
• Describe the decibel calibration for measuring sound intensity
• Solve problems involving the intensity of a sound moving ridge
• Draw how humans produce and hear sounds

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Teacher Support

The learning objectives in this section volition help your students chief the following standards:

• (7) Science concepts. The student knows the characteristics and beliefs of waves. The student is expected to:
  • (C) compare characteristics and behaviors of transverse waves, including electromagnetic waves and the electromagnetic spectrum, and characteristics and behaviors of longitudinal waves, including sound waves;
  • (F) describe the role of wave characteristics and behaviors in medical and industrial applications.

Section Fundamental Terms

amplitude	decibel	hearing	loudness
pitch	sound intensity	sound intensity level

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[BL] Review sound, properties of sound waves and characteristics of sound waves.

Aamplitude, Loudness and Energy of a Sound Wave

Figure 14.9 Racket on crowded roadways like this one in Delhi makes it hard to hear others unless they shout. (Lingaraj G J, Flickr)

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Misconception Alert

Students may be confused betwixt amplitude and intensity. While sound intensity is proportional to aamplitude, they are different concrete quantities. Sound intensity is defined equally the sound power per unit area, whereas amplitude is the distance between the resting position and the crest of a wave.

In a quiet wood, you can sometimes hear a single leaf fall to the ground. Simply in a traffic jam filled with honking cars, y'all may have to shout just then the person next to you tin can hear Figure fourteen.ix.The loudness of a audio is related to how energetically its source is vibrating. In cartoons showing a screaming person, the cartoonist often shows an open mouth with a vibrating uvula (the hanging tissue at the back of the oral cavity) to represent a loud audio coming from the throat. Effigy xiv.10 shows such a drawing depiction of a bird loudly expressing its stance.

A useful quantity for describing the loudness of sounds is called sound intensity. In general, the intensity of a wave is the power per unit surface area carried by the moving ridge. Power is the charge per unit at which energy is transferred by the wave. In equation form, intensity I is

where P is the power through an area A. The SI unit of measurement for I is W/one thousand². The intensity of a sound depends upon its force per unit area amplitude. The relationship between the intensity of a audio wave and its force per unit area amplitude (or pressure variation Δp) is

$$I=\frac{{\left(\Delta p\right)}^{\mathrm{ii}}}{2\rho v_w}\text{,}$$

14.6

where ρ is the density of the material in which the sound wave travels, in units of kg/m^three, and v is the speed of sound in the medium, in units of thousand/s. Pressure level aamplitude has units of pascals (Pa) or N/grand². Annotation that Δp is half the difference between the maximum and minimum force per unit area in the audio wave.

We can encounter from the equation that the intensity of a sound is proportional to its amplitude squared. The pressure variation is proportional to the aamplitude of the oscillation, so I varies equally (Δp)². This relationship is consequent with the fact that the audio wave is produced by some vibration; the greater its pressure amplitude, the more the air is compressed during the vibration. Because the power of a audio moving ridge is the rate at which energy is transferred, the free energy of a sound wave is also proportional to its amplitude squared.

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[OL] [AL] Notation from the equation that the intensity of sound is also affected past the density of the cloth that it travels through. The denser the material, the lower the intensity of sound.

Tips For Success

Pressure is usually denoted past majuscule P, but we are using a lowercase p for force per unit area in this case to distinguish it from ability P to a higher place.

Effigy 14.10 Graphs of the pressures in ii sound waves of different intensities. The more intense audio is produced by a source that has larger-amplitude oscillations and has greater pressure level maxima and minima. Because pressures are higher in the greater-intensity sound, information technology tin can exert larger forces on the objects information technology encounters.

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Instructor Support

[BL] [OL] [AL] Ask students whether the pitch of both birds differs. How can they tell by looking at the graph?

The Decibel Scale

You may accept noticed that when people talk about the loudness of a sound, they depict information technology in units of decibels rather than watts per meter squared. While sound intensity (in Westward/1000²) is the SI unit, the sound intensity level in decibels (dB) is more relevant for how humans perceive sounds. The way our ears perceive sound tin can exist more accurately described by the logarithm of the intensity of a sound rather than the intensity of a sound directly. The sound intensity level β is defined to exist

$$\beta \text{ (dB)}=10{\text{ log}}_{10}\left(\frac{I}{I_0}\right)\text{,}$$

14.7

where I is sound intensity in watts per meter squared, and I ₀ = x^–12 Due west/mⁱⁱ is a reference intensity. I ₀ is chosen as the reference point because it is the lowest intensity of sound a person with normal hearing can perceive. The decibel level of a sound having an intensity of 10^–12 W/chiliadⁱⁱ is β = 0 dB, considering log₁₀ 1 = 0. That is, the threshold of human hearing is 0 decibels.

Each factor of 10 in intensity corresponds to 10 dB. For example, a 90 dB sound compared with a 60 dB audio is thirty dB greater, or three factors of 10 (that is, 10³ times) every bit intense. Some other example is that if i sound is 10^vii as intense as another, it is lxx dB college.

Since β is defined in terms of a ratio, it is unit-less. The unit called decibel (dB) is used to indicate that this ratio is multiplied past ten. The sound intensity level is non the same as sound intensity—information technology tells you the level of the sound relative to a reference intensity rather than the bodily intensity.

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[BL] [OL] [AL] Note that decibel is different from other units in that it is not an absolute measurement. It is a ratio of two measurements. It is useful, and more widely used because it is closer to how humans perceive sound.

Snap Lab

Feeling Sound

In this lab, you volition play music with a heavy beat to literally feel the vibrations and explore what happens when the volume changes.

• CD player or portable electronic device connected to speakers
• rock or rap music CD or mp3
• a lightweight table

Process

1. Identify the speakers on a light table, and offset playing the CD or mp3.
2. Identify your hand gently on the table next to the speakers.
3. Increase the volume and note the level when the table only begins to vibrate as the music plays.
4. Increment the reading on the volume control until it doubles. What has happened to the vibrations?

Do you think that when you double the volume of a sound wave you are doubling the sound intensity level (in dB) or the audio intensity (in \text{W}/\text{m}^{2})? Why?

1. The audio intensity in \text{West}/\text{thousand}^2, because it is a closer measure of how humans perceive audio.

2. The sound intensity level in \text{dB} considering it is a closer measure of how humans perceive sound.

3. The sound intensity in \text{West}/\text{grand}^two because information technology is the only unit to limited the intensity of sound.

4. The sound intensity level in \text{dB} considering information technology is the only unit to express the intensity of audio.

Solving Sound Wave Intensity Problems

Worked Example

Calculating Sound Intensity Levels: Sound Waves

Summate the sound intensity level in decibels for a sound wave traveling in air at 0 ºC and having a pressure amplitude of 0.656 Pa.

Strategy

We are given Δp, so we can calculate I using the equation $I=\frac{{\left(\Delta p\right)}^{\mathrm{two}}}{2\rho v_{}}$ . Using I , nosotros can calculate β direct from its definition in $\beta \text{ (}d\text{B)}=10{\mathrm{ log}}_{10}\left(\frac{I}{I_0}\right)$ $\beta \text{ (dB)}=10{\text{ log}}_{10}\left(\frac{I}{I_0}\right)$ .

Give-and-take

This 87.0 dB sound has an intensity five times as great as an lxxx dB sound. So a cistron of five in intensity corresponds to a difference of seven dB in audio intensity level. This value is true for any intensities differing by a factor of five.

Worked Instance

Modify Intensity Levels of a Sound: What Happens to the Decibel Level?

Show that if i audio is twice as intense as another, it has a sound level near three dB higher.

Strategy

You are given that the ratio of two intensities is 2 to ane, and are and then asked to notice the difference in their sound levels in decibels. You lot can solve this trouble using of the properties of logarithms.

Discussion

This ways that the ii sound intensity levels differ by 3.01 dB, or well-nigh 3 dB, as advertised. Note that because only the ratio I _two/I ₁ is given (and non the actual intensities), this effect is truthful for any intensities that differ by a factor of two. For instance, a 56.0 dB sound is twice as intense equally a 53.0 dB sound, a 97.0 dB audio is one-half as intense equally a 100 dB audio, and so on.

Practice Problems

7 .

Calculate the intensity of a wave if the power transferred is x West and the area through which the moving ridge is transferred is 5 square meters.

1. 200 W / m²
2. fifty Due west / m²
3. 0.five West / k²
4. 2 W / grand²

eight .

Calculate the sound intensity for a sound wave traveling in air at 0^{\circ}\text{C} and having a pressure amplitude of 0.ninety\,\text{Pa}.

1. i.8\times 10^{-3}\text{W}/\text{m}^two

2. 4.2\times 10^{-iii}\,\text{Westward}/\text{m}^{2}

3. i.1\times x^{3}\,\text{Westward}/\text{m}^two

4. 9.v \times ten^{-4}\,\text{West}/\text{m}^ii

Hearing and Voice

People create sounds past pushing air up through their lungs and through elastic folds in the throat called vocal cords. These folds open and close rhythmically, creating a pressure buildup. Equally air travels up and past the vocal cords, it causes them to vibrate. This vibration escapes the mouth along with puffs of air every bit sound. A phonation changes in pitch when the muscles of the larynx relax or tighten, changing the tension on the vocal chords. A vocalization becomes louder when air menstruum from the lungs increases, making the amplitude of the sound pressure wave greater.

Hearing is the perception of sound. Information technology can give us plenty of information—such equally pitch, loudness, and direction. Humans can normally hear frequencies ranging from approximately 20 to twenty,000 Hz. Other animals have hearing ranges dissimilar from that of humans. Dogs tin can hear sounds every bit high every bit 45,000 Hz, whereas bats and dolphins can hear up to 110,000 Hz sounds. You may take noticed that dogs respond to the sound of a domestic dog whistle which produces sound out of the range of human hearing.

Sounds below 20 Hz are chosen infrasound, whereas those above twenty,000 Hz are ultrasound. The perception of frequency is called pitch, and the perception of intensity is called loudness.

The mode nosotros hear involves some interesting physics. The sound wave that hits our ear is a pressure moving ridge. The ear converts audio waves into electrical nerve impulses, similar to a microphone.

Figure fourteen.eleven shows the anatomy of the ear with its division into 3 parts: the outer ear or ear culvert; the centre ear, which runs from the eardrum to the cochlea; and the inner ear, which is the cochlea itself. The body part normally referred to as the ear is technically called the pinna.

Figure 14.11 The illustration shows the anatomy of the human ear.

The outer ear, or ear canal, carries sound to the eardrum protected inside of the ear. The middle ear converts sound into mechanical vibrations and applies these vibrations to the cochlea. The lever organisation of the center ear takes the force exerted on the eardrum by sound pressure variations, amplifies it and transmits it to the inner ear via the oval window. Two muscles in the middle ear protect the inner ear from very intense sounds. They react to intense sound in a few milliseconds and reduce the force transmitted to the cochlea. This protective reaction can also be triggered past your ain vox, so that humming during a fireworks display, for example, can reduce noise damage.

Effigy 14.12 shows the centre and inner ear in greater item. As the middle ear bones vibrate, they vibrate the cochlea, which contains fluid. This creates pressure waves in the fluid that cause the tectorial membrane to vibrate. The motion of the tectorial membrane stimulates tiny cilia on specialized cells chosen hair cells. These hair cells, and their fastened neurons, transform the motility of the tectorial membrane into electric signals that are sent to the brain.

The tectorial membrane vibrates at different positions based on the frequency of the incoming sound. This allows united states of america to discover the pitch of audio. Additional processing in the brain too allows us to determine which direction the sound is coming from (based on comparison of the sound's arrival fourth dimension and intensity between our two ears).

Effigy 14.12 The inner ear, or cochlea, is a coiled tube about 3 mm in bore and 3 cm in length when uncoiled. As the stapes vibrates confronting the oval window, it creates pressure waves that travel through fluid in the cochlea. These waves vibrate the tectorial membrane, which bends the cilia and stimulates nerves in the organ of Corti. These nerves so send information well-nigh the sound to the encephalon.

Fun In Physics

Musical Instruments

Figure 14.thirteen Playing music, also known as "rocking out", involves creating vibrations using musical instruments. (John Norton)

All the same another way that people make sounds is through playing musical instruments (see the previous figure). Call back that the perception of frequency is called pitch. Y'all may accept noticed that the pitch range produced past an instrument tends to depend upon its size. Small instruments, such equally a piccolo, typically brand high-pitch sounds, while larger instruments, such as a tuba, typically make depression-pitch sounds. High-pitch means modest wavelength, and the size of a musical musical instrument is directly related to the wavelengths of sound it produces. So a pocket-sized instrument creates brusk-wavelength sounds, only equally a big instrument creates long-wavelength sounds.

Most of u.s. have splendid relative pitch, which means that we tin can tell whether one audio has a different frequency from some other. We tin unremarkably distinguish 1 audio from another if the frequencies of the ii sounds differ past as little as 1 Hz. For case, 500.0 and 501.5 Hz are noticeably different.

Musical notes are detail sounds that tin be produced by about instruments, and are the building blocks of a song. In Western music, musical notes accept detail names, such as A-precipitous, C, or E-flat. Some people can identify musical notes just by listening to them. This rare ability is called perfect, or absolute, pitch.

When a violin plays centre C, in that location is no mistaking it for a piano playing the same note. The reason is that each musical instrument produces a distinctive set of frequencies and intensities. We telephone call our perception of these combinations of frequencies and intensities the timbre of the sound. Information technology is more than difficult to quantify timbre than loudness or pitch. Timbre is more than subjective. Evocative adjectives such as dull, brilliant, warm, cold, pure, and rich are used to describe the timbre of a sound rather than quantities with units, which makes for a difficult topic to dissect with physics. So the consideration of timbre takes us into the realm of perceptual psychology, where higher-level processes in the encephalon are dominant. This is also true for other perceptions of audio, such as music and noise. But as a teenager, you are likely already aware that one person'south music may be another person's racket.

If you turn up the book of your stereo, volition the pitch change? Why or why non?

1. No, because pitch does not depend on intensity.

2. Yeah, because pitch is direct related to intensity.

Check Your Understanding

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Use these questions to assess student achievement of the department'southward Learning Objectives. If students are struggling with a specific objective, these questions will aid place which and direct students to the relevant content.

nine .

What is sound intensity?

1. Intensity is the free energy per unit area carried past a moving ridge.

2. Intensity is the energy per unit volume carried by a wave.

3. Intensity is the power per unit area carried by a wave.

4. Intensity is the power per unit volume carried past a wave.

10 .

How is ability defined with reference to a sound moving ridge?

1. Power is the rate at which energy is transferred past a sound wave.

2. Power is the rate at which mass is transferred by a sound moving ridge.

3. Power is the charge per unit at which amplitude of a sound wave changes.

4. Power is the rate at which wavelength of a audio wave changes.

11 .

What word or phrase is used to describe the loudness of sound?

1. frequency or oscillation
2. intensity level or decibel
3. timbre
4. pitch

12 .

What is the mathematical expression for sound intensity level \beta?

1. \beta\left(\text{dB}\right)=x\log_{10}\left(\frac{I_0}{I}\right)

2. \beta\left(\text{dB}\right)=xx\log_{10}\left(\frac{I}{I_0}\right)

3. \beta\left(\text{dB}\right)=20\log_{10}\left( \frac{I_0}{I}\right)

4. \beta\left(\text{dB}\right)=10\log_{x}\left(\frac{I}{I_0}\right)

13 .

What is the range of frequencies that humans are capable of hearing?

1. 20 Hz to 200,000 Hz

2. 2 Hz to 50,000 Hz

3. ii Hz to 2,000 Hz

4. 20 Hz to 20,000 Hz

14 .

How practice humans change the pitch of their voice?

1. Relaxing or tightening their glottis
2. Relaxing or tightening their uvula
3. Relaxing or tightening their natural language
4. Relaxing or tightening their larynx

References

Nave, R. Vocal sound production—HyperPhysics. Retrieved from http://hyperphysics.phy-astr.gsu.edu/hbase/music/voice.html

jonesandla1992.blogspot.com

Source: https://openstax.org/books/physics/pages/14-2-sound-intensity-and-sound-level

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