Page 14 - 11-phy-8 Waves

8. Waves eLearn.Punjab

Putting the values of ro in equation 8.8 we have,

v=t 1+ t ........... (8.9)
vo 273 (8.10)

or =vt =273 + t T ..........
vo 273 To

where T and T0 are the absolute temperatures corresponding to t°C and 0 °C respectively. Thus, the

speed of sound varies directly as the square root of absolute

temperature. Expanding the R.H.S. of equation (8.9), using Tidbits

Binomial theorem and neglecting higher powers, we have

vt =(1+ t ) or vt =vo + 5v4ot6
vo 546
As vo = 332ms-1.
putting this value in the 2nd factor

Then v=t vo + 332 t
or 546

v=t vo + 0.61 t ......... (8.11)

Example 8.1: Find the temperature at which the velocity of

sound in air is two times its velocity at 10 °C.

Solution : 10oC = 10oC + 273 = 283K
Suppose at T K,the velocity is two times its value
at 283K.

Since vt = T
v283 283K
What happens when a jet plane like Concorde
Therefore, vt = T = 2 flies faster than the speed of sound?
or v283 283K
T = 1132K or 859 oC A conical surface of concentrated sound
energy sweeps over the ground as a
14 supersonic plane passes overhead. It is
known as sonicboom.

v: 1.1