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

_{1 }/ v

_{2}= √T

_{1 }/ T

_{2}

Squaring both sides we get :

(v

_{1}/ v

_{2})

^{2}= T

_{1}/ T

_{2 }--- (i)

Let v

_{1}is the speed at 27 C , and v

_{2}be the speed at new temperature, So according to the given data:

v

_{2}= 2v

_{1}

using the value of v

_{2}in equation (i) we get:

(v

_{1 }/ 2v1 )

^{2}= T

_{1 }/ T

_{2 }

this gives:

(1/2)

^{2}= T

_{1 }/ T

_{2 }

this gives:

T

_{2}= 4 T

_{1}

where T

_{1}is initial temperature which equals 300 K

so we get,

T

_{2}= 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:

**T**

_{2}= k^{2}( T_{1}+ 273 ) - 273Here k is the factor which depends how much change in the speed we want.

Remember in this formula T

_{1}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 T

_{1}=27 C

so T

_{2}= 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..

thanks :)

ReplyDeletesuperb (y)

ReplyDelete:)

ReplyDelete(Y)

ReplyDeletekia yeh shrt cut tha :P

ReplyDeletejee :p u have to use the end result only :p

ReplyDeletepaper me sari derivation to nae karni pehlay :p

Ajeeb shortcut hain ...

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