382
8 Waves
(c) E =
I
v
E 1
E 2
=
I 1
I 2
v 2
v 1
=
8
9
×
2
3
=
16
27
8.66 (a) λ =
v
f
∴
λ A
λ W
=
v A
v W
=
331
1450
= 0.228 (∵ f A = f W )
(b) P max =
√
2Iρ 0 v
∴
P A
P W
=
ρ A
ρ W
v A
v W
=
1.293
1000
×
331
1450
= 0.0172 (∵ I A = I W )
(c) A =
2I
ρvω 2
A A
A W
=
ρ W
ρ A
v W
v A
=
1000
1.293
×
1450
331
= 33.88 (∵ I A = I W and f A = f w )
8.67 Characteristic impedance of a gas
Z = ρ 0 v
(1)
Now v =
B
ρ 0
or ρ 0 =
B
v 2
∴ Z =
B
v
= B
M
γ RT
(2)
Thus Z ∝
1
√
T
(a) At 0 ◦ C, v = 331 m/s, ρ 0 = 1.293 kg/m
3
Z = ρ 0 v = 1.293 × 331 = 428 rayl
(b) Z ∝
1
√
T
∴ Z (80
◦ C) = Z (0
◦ C) ×
273
273 + 80
= 428 × 0.879 = 376 rayl
8 Waves
(c) E =
I
v
E 1
E 2
=
I 1
I 2
v 2
v 1
=
8
9
×
2
3
=
16
27
8.66 (a) λ =
v
f
∴
λ A
λ W
=
v A
v W
=
331
1450
= 0.228 (∵ f A = f W )
(b) P max =
√
2Iρ 0 v
∴
P A
P W
=
ρ A
ρ W
v A
v W
=
1.293
1000
×
331
1450
= 0.0172 (∵ I A = I W )
(c) A =
2I
ρvω 2
A A
A W
=
ρ W
ρ A
v W
v A
=
1000
1.293
×
1450
331
= 33.88 (∵ I A = I W and f A = f w )
8.67 Characteristic impedance of a gas
Z = ρ 0 v
(1)
Now v =
B
ρ 0
or ρ 0 =
B
v 2
∴ Z =
B
v
= B
M
γ RT
(2)
Thus Z ∝
1
√
T
(a) At 0 ◦ C, v = 331 m/s, ρ 0 = 1.293 kg/m
3
Z = ρ 0 v = 1.293 × 331 = 428 rayl
(b) Z ∝
1
√
T
∴ Z (80
◦ C) = Z (0
◦ C) ×
273
273 + 80
= 428 × 0.879 = 376 rayl