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Sunday, October 27

Speed of Sound

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
a.273 C
b.0 C
c.927 C
d.1027 C

First of all see the traditional way of solving the problem which all follow:

Step 1: 
Conversion of centigrade to Kelvin:

                                           27 C = (27 + 273) K = 300K

Step 2:
Using the formula:

                                                  v/ v2 = √T/ 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:

                                                 (v/ 2v1 )2 = T/ T2   
this gives:

                                                   (1/2)2 = T/ T2   

this gives:
                                                      T2 = 4 T1

where T1 is initial temperature which equals 300 K
 so we get,
                                                     T2 = 1200K

Step 3:
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..


  1. Šÿêdå Fòžïã Šhäh Kâžmî1 November 2013 at 02:29


  2. kia yeh shrt cut tha :P

  3. jee :p u have to use the end result only :p
    paper me sari derivation to nae karni pehlay :p

  4. Said Nawaz Ghori5 April 2014 at 21:10

    Ajeeb shortcut hain ...


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