2.972 How Speakers Work

SPEAKERS
QUESTIONS OR COMMENTS

	AUTHOR:	Roman M. Luz III
	E-MAIL:	luzman@mit.edu
	COURSE:	2
	CLASS/YEAR:	2

MAIN FUNCTIONAL REQUIREMENT: Convert electric signal into audible sound.

DESIGN PARAMETER: Loudspeaker (there are other types of speakers . . .)

GEOMETRY/STRUCTURE:


Full View of Speaker	Speaker Components

Typical speaker cones range from 1.5 to 18 inches in diameter. Speakers of this size can consume from 0.25-250 Watts (W), resonate at a frequency of 16-4kHz, and have a sensitivity level of up to 95 Decibels (dB)

	Magnet Structure -- Two pieces of oppositely oriented magnets that produce a radial field from the inner to outer magnet
	Voice Coil -- Carries the current so that it is always moving in a plane perpindicular to the magnetic field; thus the force always acts on the same axis
	Spider -- Vibrates rigidly with the voice coil and translates the mechanical energy to the cone
	Cone -- Produces pressure waves from its surface due to the oscillation of the spider
	Basket -- Holds the components together firmly, preventing motion in parts like the magnet structure
	Dust Cap -- Protects the cone and circuitry from dust . . . a clean speaker is a happy speaker :)

EXPLANATION OF HOW IT WORKS/ IS USED:

**The waves propagating from the cone seen here only represent sound waves (real sound waves do not look like these)

Animation of Speaker Operation

The electric signal passes through the wire in the form of an analog, sinusoidal (or other) wave

The signal enters the voice coil, wrapping around the inner magnet (in the form of a solenoid)

A force is exerted from the stable magnet structure to the free-moving voice coil

As the signal's amplitude and frequency change, the force on the voice coil undulates back and forth

The voice coil rapidly vibrates along the axis of the magnet structure, thereby vibrating the cone

As the voice cone vibrates, the air immediately around it is pressurized and rarified.

The pressurized air molecules propagate as a wave -- this is sound

DOMINANT PHYSICS:

Variable	Description	Metric Units	English Units
P_in	Electric Power in wires	Watts	Horsepower
P_out	Acoustic Power in sound wave	Watts	Horsepower
P_loss	Power loss (in circuits and air)	Watts	Horsepower
V	Voltage difference across the voice coils	Volts	Volts
i	Current in coils	Amperes	Amperes
B	Magnetic Field	Farads	Farads
F_mechanical	Force exerted on the voice coil by the magnetic field	Newtons	lbf
vc	Velocity of voice coil	m/s	mph
Dp	Pressure difference across sound wave	Pascals	lbf/in²
A	Area of pressure wave	m²	ft²
vw	Velocity of pressure wave	m/s	mph
h	Efficiency	---	---

The speakers are powered by entering current and voltage:
P_in = V i
    **All speakers use amplifiers to add more current to the signal to produce louder sound
    **i is a function of time, i(t), whose average value is its maximum amplitude divided by the square root of two

The constant magnetic field acting on this current produces a force on the voice coil:
F = i x B (where i and B are vectors)

The force accelerates the voice coil and the power is converted to mechanical power:
F = m a = m dvc/dt
P = F vc

The coils vibrate the cone, which produces a pressure wave that carries the acoustic power:
F = p A
P_out = vw A Dp

or, another way of looking at the power exiting the system is:
P_out = P_in - P_loss = hP_in
    **This is from the definition for efficiency

AMPLIFIERS
Amplifiers are needed to boost the current source because the current originally carrying the signal is too weak to render audible sound. Amplifiers use transistors to allow a weak signal to depict the form of a much stronger signal. In this way, the amplifier takes in a signal of a certain frequency and amplitude and puts out a signal with the same frequency, but much larger amplitude.

SIGNALS
The way a signal corresponds to a sound is through its frequency and amplitude. The frequency relates to how fast the cone oscillates. A high frequency (fast movement) produces a high pitch, and a low frequency (slow movement) produces a deep pitch. The amplitude simply tells the cone how hard to push. This "pushing force" corresponds to the pressure difference in the wave, which corresponds to the volume of the sound.

LIMITING PHYSICS:

EFFICIENCY
Loudspeakers are incredibly inefficient. They can only convert 0.5% to 2% of the power they consume into acoustic power. Most of the energy lost is given off as heat emanating from the voice coil and other electric circuits inside the speaker. In particular, one group of circuits, called the crossover, dissipates a large percent (how much?) of the energy. The crossover is comprised of capacitors, resistors, and inductors, and it has the function of sending high frequency signal to the tweeter and low frequency to the woofer. All of these circuit components take some electric power and convert it to heat.

PLOTS/GRAPHS/TABLES:

None Submitted

WHERE TO FIND SPEAKERS:

Everywhere! They are all around us -- in our TV's, computers, alarm clocks, cars, stereos, headphones, etc.

Car speakers

TV speakers

General speakers

Horn speakers

REFERENCES/MORE INFORMATION:

Interview: Niels Braroe, MIT Lecturer, January 13, 5:30PM, in the MIT Hobby Shop

Interview: Noah Bray-Ali, MIT Physics Major, January 12, 6:00PM, in Alpha Delta Phi fraternity of MIT

Electroacoustics: Microphones, Earphones, and Loudspeakers; Gayford, M. L.; American Elsevier Publishing Company Inc., New York 1971

LINKS

Complete Computer Solutions

How to Make Loudspeakers

ELECTROSTATIC LOUDSPEAKERS

Electrodynamic Loudspeakers