Chapter 8 :Waves
Long Question :
On which factor speed of sound depend? Derive Newton′s Formula to calculate speed of sound .Also derive Laplace Correction.
Answer:
Factors Depends on speed of sound:::::
(1) Elasticity ( E ) which would be reciprocal of compressibility.
(2) Inertia / Density ( ρ ).
____________
V=√ E
----------- → (1)
ρ
Newton′s Formula :
According to Boyel′s Law
PV=Constant.
∴P→p+Δp
∴V→V-Δy
pv=[p+Δp][v-Δv]
pv=pv-pΔv+Δpv-ΔpΔv ∴ Δ×Δ=Δ²
Neglecting higher power Δ².......
pv=pv - pΔv+Δpv
pv-pv= -pΔv+Δpv
0= -pΔv +Δpv
pΔv = Δpv
Δpv Δp
p= ---------- ∴ p=--------
Δv Δv/v
Δpv
∴ p=-----------
Δv
Δp ( Elastic stress)
p= ----------
Δv/v ( Elastic strain).
p= E ( Elasticity).
put in (1)
_________
v=√ p
--------
ρ
∴ p= 101235 Nm-²
Or 1.0×10³+²Nm-²
ρ=1.29 kgm-³
_______________
v=√ 1.0 ×10 ³+²
------------------
1.29
V=280 ms-1
