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Math Help - Bats emit sounds...

  1. #1
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    Bats emit sounds...

    Bats emit sounds of frequencies around 35.0 kHz and use echolocation to find their prey. If a bat is moving at the speed of 12.0 m/s toward an insect at an air temperature of 20.0oC, (assume the insect and air are still)
    (a) What frequency is heard by the insect?
    (b) What frequency is heard by the bat from the reflected sound?
    (c) Would the speed of the bat affect the answers?
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  2. #2
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    Quote Originally Posted by tacubo
    Bats emit sounds of frequencies around 35.0 kHz and use echolocation to find their prey. If a bat is moving at the speed of 12.0 m/s toward an insect at an air temperature of 20.0oC, (assume the insect and air are still)
    (a) What frequency is heard by the insect?
    (b) What frequency is heard by the bat from the reflected sound?
    (c) Would the speed of the bat affect the answers?
    a) As the speed of the bat is very much less than the speed of sound, we have
    the frequency as heard by the insect would be:

    <br />
f=f_0(1+\frac{20}{c})<br />

    that is there is an up-Doppler shift (This is in \mbox{kHz} if f_0 is in \mbox{kHz}).

    b) The up-shift is twice that heard by the insect so the frequency heard by
    the bat is:

    <br />
f=f_0(1+2\frac{20}{c})<br />

    c) It depends only on the closing speed (as long as this is very much less
    than the sped of sound).

    Look at your notes for the sound speed dependence of temperature , it should
    be something like:

    c=331.4+0.6 T_c\ \mbox{m/s},

    where T_c is the temperature in Celsius.

    RonL

    Note: Bats often transmit a wideband chirp with a bandwidth much greater
    than the targets Doppler, which as a result is virtually unobservable. But the
    result is that the range can be measured with greater precision that the
    pulse length, which itself can be longer in consequence so that a single
    transmissions can contain more energy increasing the detection range,
    and resistance to moth jamming signals.

    Bio-sonar:- a subject more facinating than you might imagine
    Last edited by CaptainBlack; August 7th 2006 at 01:37 PM.
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    Quote Originally Posted by CaptainBlank
    Doppler shift
    I am confused about something. It deals with the speed of light.

    If a train is traveling and a light source is emmitted it still travels at the same speed. The same as though a train is at rest. (Special Relativity right?).

    However, can you explain Hubble's observations? Red shifting and Blue shifting galaxies depending whether they are approaching us are going away from us. This is the Doppler Shift in effect. Now when we are dealing with sound the doppler shift makes sense because it is a not the speed of light. But how would you explain the blue and red shift in the visible spectrum because it travels at the speed of light. Thus, the light of the galaxy cannot effect the wavelength of light because it is still the same. Understand my problem?
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    Quote Originally Posted by ThePerfectHacker
    I am confused about something. It deals with the speed of light.

    If a train is traveling and a light source is emmitted it still travels at the same speed. The same as though a train is at rest. (Special Relativity right?).

    However, can you explain Hubble's observations? Red shifting and Blue shifting galaxies depending whether they are approaching us are going away from us. This is the Doppler Shift in effect. Now when we are dealing with sound the doppler shift makes sense because it is a not the speed of light. But how would you explain the blue and red shift in the visible spectrum because it travels at the speed of light. Thus, the light of the galaxy cannot effect the wavelength of light because it is still the same. Understand my problem?
    Its a time dialtion effect.

    (In fact the equations are identical for sound - the speed of the transmitter
    and reciever with respect to the medium do not enter the calculation only
    the component of relative velocity along the line of sound. For at least some
    of my calculations in my job in real life I use the full relativistic model,
    which is a pure time dilation even though we are dealing with sound. That is
    the frequency change is obtained more accuratly with a relativistic time
    dilation, and this also produces the required shortening or stretching of the
    echo pulse).

    RonL
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    Quote Originally Posted by ThePerfectHacker
    If a train is traveling and a light source is emmitted it still travels at the same speed. The same as though a train is at rest. (Special Relativity right?).
    I don't mean to be a prig, but I have to nitpick this. A train cannot go the speed of light. It can go just below the speed of light, however, meaning a v = (0.9999999...)c. In this case, yes, the light emitted leaves the train at the speed of light according to an observer on the train. (According to any observer at any point or speed, in fact.)

    Quote Originally Posted by ThePerfectHacker
    However, can you explain Hubble's observations? Red shifting and Blue shifting galaxies depending whether they are approaching us are going away from us. This is the Doppler Shift in effect. Now when we are dealing with sound the doppler shift makes sense because it is a not the speed of light. But how would you explain the blue and red shift in the visible spectrum because it travels at the speed of light. Thus, the light of the galaxy cannot effect the wavelength of light because it is still the same. Understand my problem?
    CaptainBlack was absolutely correct about the Doppler effect as it applies to Special Relativity. I would like to add a few comments about it, however. (Completely out of character, of course. ) Anyway, what the heck is a red/blue shift and how does it come about? Since light can only leave an object at the speed of light and be observed moving at the speed of light, the speed of the source has no effect on the speed of the light waves. What it DOES do though, is change the energy value of that light wave. As the light wave leaves, say, a distant galaxy that is moving away from us what happens is that the frequency of the light is decreased (or the wavelength is lengthened, however you wish to view it), and since E = hf, the observed energy of the light is decreased from what it would ordinarily be. A decreasing frequency is a shift toward the red end of the spectrum, so "red shift." (This whole argument, by the way, is similar to the description of why a moving sound source comes in at a lower frequency than normal, the only difference is that here the light wave is still travelling at c so the SR light wave Doppler equation looks slightly different. The point is that the pictures we use to analyze the non-relativistic Doppler effect more or less still apply. Yeah, there's a time dilation effect, but I'm trying to keep it simple! )

    By the way, the SR Doppler effect explains why there is a "background" temperature of the Universe of about 3 - 4 K. Several minutes after the big bang the Universe was, (very) simply put, a fireball. The light emitted from that fireball expanded outward and is now being observed from the edge of the Universe. That light, coming from such a large distance from a source moving at near the speed of light (according to Hubble's Law), has been enormously red-shifted to a very low frequency, which we can translate into an energy using E = hf, and then to a temperature by E = kT, where k is Boltzmann's constant.

    -Dan
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    I understood very little from what you said. Anyway +rep+
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