Resonance

Sound Intensity and Resonance

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Objectives

• Calculate the intensity of sound.

• Relate intensity, decibel level, and perceived loudness.

• Explain why resonance occurs.

Sound Intensity

When a piano player strikes a piano key, a hammer inside the piano strikes a wire and causes it to vibrate. The wire's vibrations are then transferred to the piano's soundboard.

Sound Intensity cont.

As the sound board vibrates, it exerts a force on air molecules around it, causing the air molecules to move. As the soundboard vibrates back and forth, its kinetic energy is converted into sound waves.

Sound Intensity Cont.

The rate at which energy is transferred through a unit area of the plane wave is called the intensity of the wave.

Multiple Choice

The rate at which energy is transferred through a unit area of the plane wave is called the wave's

• force

• intensity

• kinetic energy

Sound Intensity cont.

Because power, P, is defined as the rate of energy transfer, intensity can also be described in terms of power. The SI unit for power is the watt.

Multiple Choice

The SI unit for power is the

• joule

• newton

• watt

Intensity of Sound Waves

• I is intensity (W/m²)

• p is power (W)

• r is distance from the source (m)

Intensity of Sound Waves

Multiple Choice

At a maximum level of loudness, the power output of a 75-piece orchestra radiated as sound is 70.0 W. What is the intensity of these sound waves to a listener who is sitting 25.0 m from the orchestra?  

$$I\ =\ \frac{P}{4\pi r^2}$$  

• $$9.81\ x\ 10^{-3}\ \frac{W}{m^2}$$  

• $$8.91\ x\ 10^{-2}\ \frac{W}{m^2}$$  

• $$8.91\ x\ 10^{-3}\ \frac{W}{m^2}$$  

Multiple Choice

How much power is radiated as sound from a band whose intensity is 1.6 x 10^-3 W/m² at a distance of 15 m?

• 4.5 W

• 5.4 W

• 3.2 W

Intensity of Sound Waves cont.

Intensity and frequency determine which sounds are audible. The softest sounds that can be heard by the average human ear occur at frequencies of about 1000 HZ and an intensity of 1.0 x 10^-12 W/m². Such a sound is said to be at the threshold of hearing.

Intensity of Sound Waves cont.

The loudest sounds that the human ear can tolerate have an intensity of about 1.0 W/m². This is known as the threshold of pain because sounds with greater intensities can produce pain in addition to hearing. Exposure about this level can cause immediate damage to the ear.

Multiple Choice

The point at which sound becomes audible is called the

• threshold of pain

• threshold of hearing

• first decibel

Multiple Choice

Sound intensity beyond this point can cause immediate damage to the ear.

• threshold of pain

• threshold of hearing

• 100th decibel

Intensity of Sound Waves cont.

Relative intensity is measured in decibels. Relative intensity is the ratio of the intensity of a given sound wave to the intensity at the threshold of hearing. This measure of loudness is referred to as the decibel level.

Intensity of Sound Waves cont.

A decibel is a dimensionless unit that describes the ratio of two intensities of sound; the threshold of hearing is commonly used as the reference intensity.

Forced Vibration and Resonance

The vibrating strings of a guitar force the bridge of the guitar to vibrate, and the bridge in turn transfers its vibrations to the guitar body. These forced vibrations are called sympathetic vibrations.

Forced Vibrations and Resonance

Vibrations at the natural frequency produce resonance. Resonance is a phenomenon that occurs when the frequency of a force applied to a system matches the natural frequency of vibration of the system, resulting in a large amplitude of vibration.

Multiple Choice

Vibrations at the natural frequency produce

• decibels

• resonance

• the threshold of hearing

Forced Vibrations and Resonance

The human ear transmits vibrations that cause nerve impulses. The human ear is divided into three sections -- outer, middle, and inner.

The Human Ear

Sound waves travel down the ear canal of the outer ear. The ear canal terminates at a this, flat piece of tissue called the ear drum.

The Human Ear

The eardrum vibrates with the sound waves and transfers these vibrations to the three small bones of the middle ear, known as the hammer, anvil, and stirrup

The Human Ear

These bones in turn transmit the vibrations to the inner ear, which contains a snail-shaped tube about 2 cm long called the cochlea. Within the cochlea are specialized hair cells that send impulses to the brain, which interprets the impulses as sounds of varying frequencies.

Multiple Choice

The three small bones (hammer, anvil, and stirrup) are found in the

• inner ear

• middle ear

• outer ear

Multiple Choice

Vibrations travel from the eardrum to the hammer, anvil, and stirrup to the

• cochlea

• outer ear

• brain

End