# Engineering Acoustics/Echolocation in Bats and Dolphins

Echolocation is a form of acoustics that uses active sonar to locate
objects. Many animals, such as bats and dolphins, use this method to
hunt, to avoid predators, and to navigate by emitting sounds and then
analyzing the reflected waves. Animals with the ability of echolocation
rely on multiple receivers to allow a better perception of the objects'
distance and direction. By noting a difference in sound level and the
delay in arrival time of the reflected sound, the animal determines the
location of the object, as well as its size, its density, and other
features. Humans with visual disabilities are also capable of applying
biosonar to facilitate their navigation. This page will focus mainly on
how echolocation works in bats and dolphins.

## Sound Reflection

!Figure 1: Reflection and Refraction of
Waves{width="300"}

When a wave hits an obstacle, it doesn\'t just stop there but rather, it
gets reflected, diffracted, and refracted. Snell\'s law of reflection
states that:

$$\frac{sin \theta_i}{c_1}=\frac{sin \theta_t}{c_2}=\frac{sin \theta_r}{c_1}$$

where the nomenclature is defined in Figure 1. The law of reflection
states the angle of incidence is equal to the angle of reflection
($\theta_i=\theta_r$) which is clearly shown in the previous equation.

In order to determine the reflection coefficient $R$, which determines
the proportion of the wave is being reflected, the acoustic impedance is
needed and is define as where $c$ is the speed of sound and $\rho$ is
the density of the medium:

:   

    :   `<big>`{=html}`<big>`{=html}$Z=\rho c$`</big>`{=html}\
        `</big>`{=html}

For fluids only, the sound reflection coefficient is defined in terms of
the incidence angle and the characteristic impedance of the two media as
\[3\]:

$$R=\frac{\frac{Z_2}{Z_1}-\sqrt{1-[n-1]\tan^2 \theta_1}}{\frac{Z_2}{Z_1}+\sqrt{1-[n-1]\tan^2 \theta_1}}\qquad$$
where $n=\left ( \frac{c_2}{c_1} \right )^2$

As for the case where medium 2 is a solid, the sound reflection
coefficient becomes \[9\]:

$$R=\frac{(r_n-\frac{r_1}{cos \theta_i})+jx_n}{(r_n+\frac{r_1}{cos \theta_i})+jx_n}\qquad$$
where $Z_n=r_n+jx_n$ is the normal specific acoustic impedance.

The law of conservation of energy states that the total amount of energy
in a system is constant therefore if it is not being reflected, it is
either diffracted, or transmitted into the second medium which may be
refracted due to a difference in refraction index. !Figure 2:
Interaural time difference and Interaural Intensity
Level{width="300"}

## Sound Localization

Sound localization denotes the ability to localize the direction and
distance of an object, or \"target\" based on the detected sound and
where it originates from. Auditory systems of humans and animals alike
use the following different cues for sound location: interaural time
differences and interaural level differences between both ears, spectral
information, and pattern matching \[8\].

To locate sound from the lateral plane (left, right, and front), the
binaural signals required are:

-   Interaural time differences: for frequencies below 800 Hz
-   Interaural level differences: for frequencies above 1600 Hz
-   Both: for frequencies between 800 and 1600 Hz

### Interaural Time Differences

!Figure 3: Shadow cast by the
head{width="300"}

Humans and many animals uses both ears to help identify the location of
the sound; this is called binaural hearing. Depending on where the sound
comes from, it will reach either the right or left ear first, therefore
allowing the auditory system to evaluate the arrival times of the sound
at the two reception points. This phase delay is the interaural time
difference. The relationship between the difference between the length
of sound paths at the two ears, $\Delta d$, and their angular position,
$\theta$, may be calculated using the equation \[1\]:

:   

    :   `<big>`{=html}`<big>`{=html}$\Delta d=r(\theta + sin \theta)$`</big>`{=html}`</big>`{=html}

where $r$ is the half distance between the ears. This is mainly used as
cue for the azimuthal location. Thus, if the object is directly in front
of the listener, there is no interaural time difference. This cue is
used at low frequencies because the size of the head is less than half
the wavelength of the sound which allows a noticeable detection in phase
delays between both ears. However, when the frequencies are below 80 Hz,
the phase difference becomes so small that locating the direction of the
sound source becomes extremely difficult.

### Interaural level difference

As the frequency increases above 1600 Hz, the dimension of the head is
greater than the wavelength of the sound wave. Phase delays no longer
allow to detect the location of the sound source. Hence, the difference
in sound level intensity is used instead. Sound level is inversely
proportional to the source-receiver distance, given that the closer you
are to the emitting sound, the higher the sound intensity. This is also
influenced greatly by the acoustic shadow cast by the head. As depicted
in Figure 3, the head blocks sound, decreasing the sound intensity
coming from the source\[4\].

## Active Sonar

Active sonar supplies their own source and then wait for echoes of the
target\'s reflected waves. Bats and dolphins use active sonar for
echolocation. The system begins with a signal produced at the
transmitter with a source level (SL). This acoustic wave has an
intensity of I(r) where r is the distance away from the source. Next,
the source signal travels to the target while gathering a transmission
loss (TL). Once arriving at the target, the fraction of the initial
source signal which is denoted by the target strength (TS), is reflected
toward the receiver. On the way to the receiver, another transmission
loss (TL\') is experienced. For a monostatic case where the source and
the receiver are located in the exact position, TL is equal to TL\',
thus, the echo level (EL) is written as \[9\]:

:   

    :   `<big>`{=html}`<big>`{=html}$EL=10\log \frac{I(r) \sigma}{I_{ref} 4 \pi}-TL'$`</big>`{=html}`</big>`{=html}

The equation for target strength is \[9\]:

:   

    :   `<big>`{=html}`<big>`{=html}$TS=10\log\frac{\sigma}{4\pi}$`</big>`{=html}`</big>`{=html}

### Reverberation

As sound is emitted, other objects in the environment can cause the
signal to be scattered creating different echoes in addition to the echo
produced by the target itself. If we look at underwater for instance,
reverberation can result from bubbles, fish, sea surface and bottom, or
planktons. These background signals mask the echo from the target of
interest, thus, it is necessary to find the reverberation level (RL) in
order to differentiate between the echo level. The equation for RL is as
follow:

$TS_R$ represents the target strength for the reverberating region and
is defined by:

:   

    :   `<big>`{=html}`<big>`{=html}$TS_R=S_v+10\log V=S_A+10\log A$`</big>`{=html}`</big>`{=html}

where \"$V$ (or $A$) is the volume (or surface area) at the range of the
target from which scattered sound can arrive at the receiver during the
same time as the echo from the desired target\" \[9\] and $S_v$
(or$S_A$) is the scattering strength for a unit volume (or a unit
surface area).

## Echolocation in Bats

!Figure 5: Echolocation in
bats{width="300"}
Bats produce sounds through their larynx, emitting them from the mouth
or some, via their nose. Their calls consist of various types: broadband
components (varies in frequencies), pure tone signals (constant
frequency), or a mix of both components. The duration of these sounds
varies between 0.3 and 100 ms over a frequency range between 14 to
100 kHz \[7\]. Each species' calls can vary and have been adapted in a
particular way due to their lifestyles and hunting habits.

The broadband components are used for hunting in a closed environment
with background noise. The short calls yield precision in locating the
target. The short rapid calls, also prevent overlapping of waves, thus,
allowing the use of interaural time difference. Pure tones signals are
used while hunting in open environments without much background noise.
The calls are longer in duration allowing bats to locate preys at
greater distances. When searching for preys, bats emit sounds 10 to 20
times per second. As they approach their target, the number of waves
emitted can reach up to 200 times per second. The usual range for
echolocation is around 17 m.

For other mammals, the interaural time difference and the interaural
intensity level are cues used only for lateral detection. However bats
can also use interaural intensity level to establish objects in the
vertical direction. This is only applicable if the signals received are
broadband. Another difference is that bats' ears are capable of moving,
thus, allowing them to change between different acoustic cues.

The sound conducting apparatus in bats is similar to that of most
mammals. However, over years of evolution, they have been adapted to
suit their needs. One of these special characteristics is the large
pinnae which serves the purpose of acoustic antennae and mechanical
amplifiers. The movement of the pinnae permits focusing of the coming
sound wave, amplifying or weakening it.

## Echolocation in Dolphins

!Figure 6: Echolocation in
Dolphins{width="350"}

The basic idea of echolocation is comparable between bats and dolphins,
however, since both animals live in such different environment, there
are specific characteristics that differ amongst them.

Dolphins use the nasal-pharyngeal area to produce various types of
sounds (clicks, burst pulses, and whistles) in order to achieve two main
functions: echolocation and communication. Clicks, slow rate pulses that
lasts 70-250 μs at a frequencies of 40 to 150 Hz, and bursts, pulses
produced at rapid rates, are primarily used for echolocation \[1\].
After the clicks have been produced, the associated sound waves travel
through the melon, the rounded area of the dolphin\'s forehead comprised
of fats. Its function is to act as an acoustic lens to focus the
produced waves into a beam, sending it ahead. At such high frequencies,
the wave doesn\'t travel very far in water, hence, echolocation is most
effective at a distance of 5 to 200 m for preys that are 5 to 15 cm in
length \[6\].

When waves get reflected after hitting an object, unlike bats that has
pinnae to direct the waves to the inner ear, dolphins receive this
signal via the fat-filled cavities of the lower jaw bones (Figure 6).
Due to the high acoustic impedance of water, these soft body tissues
also have a similar impedance allowing sound waves to travel to the
inner ear without being reflected. Sound is then conducted to the middle
ear and inner ear, from which is then transferred to the brain.

## References

\[1\] Au, W. W. L., Popper, A. N., & Fay, R. R. (2000). Hearing by
whales and dolphins. Springer handbook of auditory research, v. 12. New
York: Springer.\
\[2\] Thomas, J. A., Moss, C., & Vater, M. (2004). Echolocation in bats
and dolphins. Chicago: The University of Chicago Press\
\[3\]Wave Reflection. (n.d.). Retrieved October 17, 2010, from
<http://www.sal2000.com/ds/ds3/Acoustics/Wave%20Reflection.htm>\
\[4\] Diracdelta.co.uk, science and engineering encyclopedia. (n.d.).
Retrieved November 6, 2010, from Interaural Level Difference:
<http://www.diracdelta.co.uk/science/source/i/n/interaural%20level%20difference/source.html>\
\[5\] Murat Aytekin, J. Z. (2007, November 27). 154th ASA Meeting, New
Orleans, LA. Retrieved November 10, 2010, from Sound localization by
echolocating bats: Are auditory signals enough?:
<http://www.acoustics.org/press/154th/aytekin.html>\
\[6\] Seaworld. (2002). Retrieved September 20, 2010, from Bottlenose
Dolphins Communication and Echolocation:
<http://www.seaworld.org/infobooks/bottlenose/echodol.html>\
\[7\] Wikipedia. (2010, February 4). Retrieved September 19, 2010, from
Animal Echolocation: <http://en.wikipedia.org/wiki/Animal_echolocation>\
\[8\] Wikipedia. (2009, March 14). Retrieved September 19, 2010, from
Sound Localization: <http://en.wikipedia.org/wiki/Sound_localization>\
\[9\] Kinsler, L. E. (1982). Fundamentals of acoustics. New York:
Wiley.\
