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Suppose a bat uses sound echoes to locate its insect prey, 3.00 m away. (See Figure $17.11 . )$ (a) Calculate the echo times for temperatures of $5.00^{\circ} C$ and $35.0^{\circ} C.$ (b) What percent uncertainty does this cause for the bat in locating the insect? (c) Discuss the significance of this uncertainty and whether it could cause difficulties for the bat. (In practice, the bat continues to use sound as it closes in, eliminating most of any difficulties imposed by this and other effects, such as motion of the prey.)

a) $t _ { 5 } = 0.018 \mathrm { s } , t _ { 35 } = 0.017 \mathrm { s }$b) $P = 5 \%$c) This definitely would caused difficulties for bat if it does not continue to use sound.

Physics 101 Mechanics

Chapter 17

Physics of Hearing

Sound and Hearing

Cornell University

Hope College

McMaster University

Lectures

08:15

In physics, sound is a vib…

02:16

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A bat moving with a speed …

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01:02

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Now we're dealing with two cases. One when the temperature is five messages on one when the temperature is 35 centuries. So let's find the time taken for the signal to come back to the back. In both cases, the back releases a signal, it says the insect and then comes back. That's so if this distance is three meters, the sound of house has to travel six meters, three meters up and three meters stone Soto the time that it takes the sound waves to travel. This will be distance by speed, which is six meters divided by the speed of some. Remember that the speed of sound it given temperature t is 331 meter per second. I'm squared off me by 2 73 k. So we use this formula at five degree says Yes, it's six meters by sea, so that's 331 meter per second time squared off 2 73 divided by T, which is 278 Kelvin because its founding this inches. In the second case, it's six meters by 3 31 meters or second. I'm squared off to 73 Kelvin Bye 200 I'm sorry. 300 eight, Kelvin. And this turns out to be 0.17 seconds. I'm sorry. This is 0.18 seconds and this is set up 1017 seconds. So the difference is zero point 001 seconds on the If you want to find the answer eternity, you divide it by the average of these two, which is 0.175 times 100 and this turns out to be about 5%. And if you multiply this with our six meters, you'll notice that 500 I'm six meters is 0.166 meters with just 16.6 centimeters. Which means because off at these two different temperatures, the bad will think off the insect as being seven, almost 17 centimeters apart, which is very bad. So if the back simply used the signal and then went on to cast the prey, it could miss by 17 30 meters. But what about us? Is it continuously sent six cents sound as it approaches the insect so it doesn't so it keeps track of the insect properly and catches it. The temperature difference is not so effective with smaller distances on. It helps the back catch its prey.

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