Here I want to share a short method which can be used to find out the speed of the sound when you make a certain temperature half, double, thrice etc .
Let's start with an example.
Q: Temperature at which speed of sound becomes double as was at 27C is
First of all see the traditional way of solving the problem which all follow:
Conversion of centigrade to Kelvin:
27 C = (27 + 273) K = 300K
Using the formula:
v1 / v2 = √T1 / T2
Squaring both sides we get :
(v1/ v2 )2 = T1/ T2 --- (i)
Let v1 is the speed at 27 C , and v2 be the speed at new temperature, So according to the given data:
v2 = 2v1
using the value of v2 in equation (i) we get:
(v1 / 2v1 )2 = T1 / T2
(1/2)2 = T1 / T2
T2 = 4 T1
where T1 is initial temperature which equals 300 K
so we get,
T2 = 1200K
Converting it back to Celsius we get
1200 K = 1200 - 273 = 927 C
In all these steps what was actually done ?
Celsius is converted into Kelvin , which is then multiplied with some factor, in last step, and then converted back to Celsius.
In mathematical form we can write the above lines as:
T2 = k2 ( T1 + 273 ) - 273
Here k is the factor which depends how much change in the speed we want.
Remember in this formula T1 is in Celsius , we are converting it in Kelvin in the brackets by adding 273...
Now applying the formula to given question:
here we have k=2 and T1 =27 C
so T2 = 4 ( 27 + 273 ) - 273 = 1200 - 273 = 927 and this is all.. Took hardly 30 sec to perform this calculation ..
Hope this will help you guys :)
In case of any confusion you can comment below..