Physics 1CLecture 14A

"Everything in the world has a spirit which is released by its sound."

--Oscar Fischinger

Quiz 1 InfoIt will be a Scantron test that covers Chapter 13.

A list of equations, constants, and conversions will be provided on the quiz.

You are to write the version of your test on the Scantron form.

You will be given a Quiz Code Number that you will be your Quiz ID for the rest of the quarter.

You are expected to abide by UC Policy on Integrity of Scholarship.

Wave Speed on a StringLet’s take the speed of the wave on a string as an example of wave speed being affected only by the medium.

How can I make the speed of the wave faster?

Make it more taut => increase the tension, FT.

Make the string less dense => decrease the mass per unit length, μ.

This will give us the following equation:

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vstring =FTµ

Wave InterferenceWhat happens if two waves on a string meet up and pass through each other?

The obey Superposition.

This means that you add together their individual displacements.

We can have either constructive interference:

Wave InterferenceOr destructive interference:

These traveling waves meet and pass through each other without being destroyed or even altered.

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Wave ReflectionsWhenever a traveling wave reaches a boundary, some or all of the wave is reflected.

When it is reflected from a fixed end, the wave is inverted.

When reflected from a free end, the pulse is not inverted.

SoundSound waves are longitudinal waves traveling through a medium.

For all sound waves:

Fluctuations in pressure/density travels through gas/liquid/solid (any medium of particles with spring-like interactions).

Source: longitudinal compression/rarefaction of medium.

SoundFor all sound waves: Source determines period, T, of the sound wave.Properties of the medium determine the speed of the sound wave, vwave. The wavelength, λ, will depend on the frequency, f, and the wave speed, vwave.

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vwave =λT

= λf

Please note that the sound medium is not moving at this speed, but the wave is propagating at this speed.

SoundFor all sound waves:

The speed of sound through a given material depends on the density of the material and how strongly the molecules in the material interact.

For a fluid that has a bulk modulus, B, and an equilibrium density, ρ, we find:

In general, the speed of sound through solids is greater than liquids and gases.

SoundAt room temperature the speed of sound through air is 343m/s. The speed of sound through water is 1,490m/s. As the temperature of a gas (such as air) changes, so does its density and, thus, so does the speed of sound in that gas.This leads to the following equation to find the speed of sound at a given temperature:

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v = 331m s( ) T273K

where 331m/s is the velocity of sound in air at 0oC and T is measured in Kelvin.

SoundSound waves can have any frequency, yet humans can only hear certain frequencies.The normal range of human hearing is between 20Hz and 20,000Hz.A sound wave with a frequency below 20Hz is known as infrasonic.Large animals, like elephants, can hear infrasonic waves.A sound wave with a frequency above 20,000Hz is known as ultrasonic.Small animals, like bats, can hear ultrasonic waves.

SoundSound waves can have any amplitude, yet humans can only hear certain amplitudes (and still have the ability to hear afterward).We measure the amplitude of a sound wave by examining how much energy is input into the wave by the source.The average intensity, I, of a wave is the time rate at which the energy flows through a given surface area, A:

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I =1AΔEΔt

=powerA

The units of intensity are Watts/m2.The direction of the energy flow is perpendicular to the surface area.

Spherical WavesA spherical wave propagates radially outward from the oscillating sphere.

The energy propagates equally in all directions.The intensity is:

The average power is the same through any spherical surface centered on the source.

Intensity will decrease as r increases.

SoundThe ear is a very sensitive detector of sound waves. It can hear a wide range of intensities.

The faintest sound that most humans can hear is called the threshold of hearing.

The threshold of hearing, Io, is 1.0x10-12 W/m2.

The loudest sound that most humans can tolerate is the threshold of pain.

The threshold of pain, Ip, is 1.0 W/m2.

Because the ear can detect such a wide range of intensities we define a new variable called the intensity level, β, that compresses the range.

SoundAs it turns out the sensation of loudness (intensity level, β) is logarithmic in the human ear.

Thus, the intensity level for a given intensity, I, is given by:

where Io is the threshold of hearing.

Intensity level is measured in deciBels, dB (a deciBel is one-tenth of a Bel).

For example, the intensity level of a jet plane is 150dB or 15Bels

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β = 10dB( ) log IIo

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SoundWhat is the intensity level of the threshold of hearing?

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β = 10dB( ) log IoIo

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β = 10dB( ) log 1( ) = 0dB

What is the intensity level of the threshold of pain?

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β = 10dB( ) logIpIo

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β = 10dB( ) log1W

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1×10−12 Wm2

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β = 10dB( ) log 1×1012( ) = 10dB( ) 12( ) =120dB

Clicker Question 14A-1You are standing 50 meters away from a source. What is the intensity level, β, of something that puts out an intensity that is ten times the threshold of hearing, (i.e. 10Io) when you are 50 meters from the source?A) 0 deciBels.

B) 1 deciBel.

C) 5 deciBels.

D) 10 deciBels.

E) 50 deciBels

For Next Time (FNT)

Study for Quiz 1

Start Chapter 14 homework after the quiz.