Suppose a bat uses sound echoes to locate its insect prey, 3.00 m away. (See Figure 17.10.) (a) Calculate the echo times for temperatures of 5.00ºC and 35.0ºC . (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.)
Bat uses echo from sound produced by it to locate prey at night, since echo distance is twice that of prey distance.
The expression to find the speed of the sound at temperature is,
Here is speed of sound, is speed of sound at and is temperature of air.
Temperature of air is, convert into kelvin.
T = + 273
= 275 K
Substitute, 331 m /s for , = 278 K for T in the above expression of speed of sound,
= (331 m/s)
= 334 m/s
The expression to find the distance d is,
Rearrange the expression for time,
Substitute 6m for d (since echo distance is twice that of prey distance) and 334 m/s for in the expression of the expression of time to find time for echo of sound at temperature .
= 0.017964 s
= (0.017964 s)
Therefore, time required to locate prey at is