Nature’s Thermometer

    蟋蟀，除了其惊人的音乐能力，并作为运气的文化符号，可以充当大自然的温度计。更具体而言，其速率啁啾与周围温度密切相关。此外，不同种类的蟋蟀会作出不同的响应温度。在此，我们使用三种不同种类的蟋蟀，在啁啾和温度的利率之间的关系进行全面研究。

    Cricket, besides its amazing ability in music and as the cultural symbols for luck, can acts as the Nature’s Thermometer. More specifically, its rate of chirp is closely related to the surrounding temperature. Also, different kinds of crickets would make different responds to the temperature. Herein, we use three types of crickets, namely the field cricket, the tree cricket and the snowy cricket, to give a comprehensive study upon the relationship between their rates of chirp and the temperature.

According to the related references and researches, we noticed that temperature can be calculated simply if we know the number of chirps in fifteen seconds, seven seconds and fourteen seconds respectively for the field crickets, tree crickets and the snowy crickets. Assume N is the number of chirps per minutes, then we can get N/4, 7N/60 and 7N/30 for the three in fifteen seconds, seven seconds and fourteen seconds. Accordingly, the functions of the temperature (T) to the number of chirps per minute (N) have been found out. To the field cricket, the function is:
T= N/4+38  (1)
To the tree cricket, the function is:
T= 7N/60+46 (2)
As for the snowy cricket, we can get:
T= 7N/30+42 (3)
Therefore, if we know exactly the number of chirps per minutes, we can use the function 1-3 to calculate the temperate. For example, if we hear each type of cricket chirps 120 times in a minute, the temperature is, for the field cricket:
T= N/4+38=120/4+38=68    (4)
For the tree cricket:
T= 7N/60+46=(7×120)/60+46=60  (5)
For the snowy cricket:
T= 7N/30+42=(7×120)/30+42=70  (6)

Since, in all three functions above, T varies according to the changes of one power of N, we can conclude that all the functions are linear functions, which can also be obviously seen in the picture 1
 
Picture 1
From the picture, we can easily learn the physical meaning of the y-intercept, which is the temperature at with the crickets fail to make sound or chirp. Since crickets no longer chirp when the temperature is above 100o, the domain for the field, tree and snowy crickets are, 0 to 248; 0 to 3240/7 and 0 to1740/7. Accordingly, the ranges of the T are 38 to 100; 46 to 100 and 42 to 100.
From the function 1-3, we can get three functions of N to T. To the field cricket:
N=4×(T-38)  (7)
To the tree cricket:
N= 60/7×(T-46)  (8)
To the snowy cricket:
N= 30/7×(T-42)  (9)
Thus, when it is 70OF, the number of chirps for each cricket is 128, 1440/7≈206 and 120. From the picture 1, we can get the intersection of the graph for the field and tree crickets. The coordination for the point is (60, 53), which physically means that at 60OF, the field and the tree cricket make the same number of chirps per minutes, 53 times per minutes.

   Sometimes, Celsius is more commonly used than Fahrenheit. Because Tc= 5/9(TF-32), when we substitute this into function (1), we can get:
Tc= 5/9 (TF-32)=5/9 (N/4+38-32)=5/9 (N/4+6)  (10)
Therefore, from the function above, we can say if we count the number of chirps in 15 seconds and add 6, the degree in Celsius is 5/9 time of the sum we get. Also, we can explain it in another way. The Degree in Celsius can be obtained by counting the number of chirps in 7.2 seconds and add 10/3.



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