Theatre Design & Technology - Summer 1983 - 12

tween frequency and wavelength is important in understanding why loudspeakers behave differently at various
frequencie . It should be evident already
that a loudspeaker capable of moving
enough air to generate a loud 38 wave
would have trouble creating the delicate
tones of a cymbal, and doing them both
well at the same time is just out of the
question.
I

Frequency

360
315

Calculating Loudness

~

-,
~

250

BEAMWIDTH
IN
DEGREES

(-6 dB)

Wave length

30----------------------------------------------------37.7 feet
60----------------------·--·----·-------·-----------18.80 feet
125------------------------------------··------------ 9.00 feet
250-------------------------------------------------- 4.50 feet
500--..--·---....----------------------------------- 2.25 feet
1000----------------·-------------------·---------13.50 inches
2000--..·--··--··----·----..---------------------- 6.75 inches
4000------------·------·------·------------------- 3.40 inches
8000---------------------------------------------- 1.70 inches
16000--..···..·------------------------------------ 0.87 inches

-

VERT.~
HOR.Q

160

125

If ~.

80

I

63

40

tI

power

In

=

=1010 (loowalls)=20dB
g
I wan
maximum SPL=95+20= 115 dB SPL
at I meter, 100 walts

A small sealed-box loudspeaker might
have a ensitivity rating of only 80 dB;
100 watts of power would produce:
80 + 20 = 100 SPL at I meter
The horn loudspeaker with a sensitivity
of 95 would require only about 3 watts
to produce 100 dB SPL at 1 meter.

3~3 )

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Applying these distance losses to our
two example loudspeakers, 100 watts at
30 feet:
The horn with a sensitivity of 95 dB
will produce:
SPL=95+ 10 loge

l~) +20 loge

;.g )

=95+20-19=96 dB SPL

Likewise, the sealed box with a sensitivity of 80 dB:
80+20-19=81 dB SPL

Typical Sound Levels
130
120
110
100
90
80

=SPL+2

i
I

Y "'0

II'

1\

I

To convert 1 meter to 4 feet:
SPL+20 10g(

,

1

i~

15 8 llllllllllB

SPL + 20 10 (referenc~ distance)
g
new dIstance

(available power in wa{(s)
og reference power in wallS

"

j

60

Sensitivity: 95 dB SPL I Wllm (I watt at I meter)
Maximum power: 100 wall

10 I

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:

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I'

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;

100

It is evident that in comparing loudspeakers, both the power and the sensitivity ratings must be considered. Often
the sensitivity rating is more important
because large differences in sensitivity
are more common than large differences
in power. Remember that a 2: 1 difference in watts (say, 50 watts vs 100
watts) is only a 3 dB difference; 50 watts
vs 200 watts is only a difference of 6 dB.
If the sensitivity is given for a distance of 4 feet, the same procedure is applied with the understanding that the
SPL will be for 4 feet rather than 1
meter. If, however, we wish to compare
two loudspeakers, one rated at 1 meter
and the other at 4 feet, we must convert
one of the ratings so that both are expressed in the same terms. SPL changes
with distance according to the formula:

. dB

~

I

III i
!

...... ~~

A loudspeaker's sensitivity rating
provides a guide to how effectively it
converts electrical power into acoustical
power. Most manufacturers list the sensitivity rating in terms of the sound pressure level (SPL) which the loudspeaker
will produce at a distance of 1 meter
when operating at a power of 1 watt.
(Some specifications still use the old
measuring distance of 4 feet, so we will
show how to apply both ratings.)
To find the SPL that will be produced by the actual power available to the
loudspeaker, first convert the power in
watts to decibels (dB) relative to 1 watt
(the rating standard), then add the
power in dB to the sensitivity rating.
For example, from the specification
sheet of a horn system:

Find the maximum SPL this loudspeaker can produce at 1 meter:

,
i

'

~

200

. I:
I:

Jet aircraft, Threshold of pain
Artillery Fire
Thunder
Elevated train
Peak music passages in a concert hall
Noisy industrial plant
Inside an airplane
Where a Hi-Fi addict is happy
Shouting as loud as possible
Inside an automobile
Loud talking

70

So we see that the SPL at 1 meter (3.3
feet) will be 2 dB greater than at 4 feet.
While I meter is the standard distance for rating sensitivity, a distance of
30 feet is more useful in anticipating
how loud the sound will be in the audience area of the theatre. We can convert
to 30 feet by applying the distance
formula:
1 m to 30 fl: SPL+20 10g( ~.g

) =SPL+(-19)

4 ftto 30 fl: SPL+20 10g( ~) =SPL+(-17)

Conversational voice
60
Office
50
40

Typical classroom
Quiet home in daytime

30

Bedroom at night

20

Rustling leaves

10

Inside special acoustical rooms

0

or empty

theatre

On a space walk, Threshold of hearing

Sound level in Decibels

SITT Summer 1983 Theatre Design & Technology

II
Table of Contents for the Digital Edition of Theatre Design & Technology - Summer 1983
