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Important Sound Waves Formulas for JEE and NEET

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 Page 1


Important Formulae 
1.  Wave Speed 
  Speed of longitudinal wave 
     
E
v ?
?
 
  (a) In solids, E = Y = Young's modulus of elasticity 
     
Y
v ?
?
 
  (b) In liquids, E = B = Bulk modulus of elasticity 
     
B
v ?
?
 
  (c) In gases, according to Newton, 
   E = B
T
 = Isothermal bulk modulus of elasticity = p 
   
p
v ?
?
 
  But results did not match with this formula. Laplace made correction in it. According to him, 
  E = B
S
 = Adiabatic bulk modulus of elasticity = ? ? 
     
p RT kT
v
Mm
? ? ?
? ? ?
?
 
2.  Effect of Temperature, Pressure and Relative Humidity in Speed of Sound in Air (or in a Gas) 
  (i) With temperature v ? T 
(ii) With pressure Pressure has no effect on speed of sound as long as temperature remains 
constant.  
(iii) With relative humidity With increase in relative humidity in air, density decreases. Hence, 
speed of sound increases. 
3.  Sound Level (L) 
   
10
0
l
L 10log
l
? (in dB) 
Here, I
0
 = intensity of minimum audible sound = 10
-12
 W m
-2
. While comparing loudness of two 
sounds we may write, 
   
2
2 1 10
1
l
L L 10log
l
?? 
  In case of point source, 
2
21
2
12
lr 1
l or
r l r
??
??
??
??
 
Page 2


Important Formulae 
1.  Wave Speed 
  Speed of longitudinal wave 
     
E
v ?
?
 
  (a) In solids, E = Y = Young's modulus of elasticity 
     
Y
v ?
?
 
  (b) In liquids, E = B = Bulk modulus of elasticity 
     
B
v ?
?
 
  (c) In gases, according to Newton, 
   E = B
T
 = Isothermal bulk modulus of elasticity = p 
   
p
v ?
?
 
  But results did not match with this formula. Laplace made correction in it. According to him, 
  E = B
S
 = Adiabatic bulk modulus of elasticity = ? ? 
     
p RT kT
v
Mm
? ? ?
? ? ?
?
 
2.  Effect of Temperature, Pressure and Relative Humidity in Speed of Sound in Air (or in a Gas) 
  (i) With temperature v ? T 
(ii) With pressure Pressure has no effect on speed of sound as long as temperature remains 
constant.  
(iii) With relative humidity With increase in relative humidity in air, density decreases. Hence, 
speed of sound increases. 
3.  Sound Level (L) 
   
10
0
l
L 10log
l
? (in dB) 
Here, I
0
 = intensity of minimum audible sound = 10
-12
 W m
-2
. While comparing loudness of two 
sounds we may write, 
   
2
2 1 10
1
l
L L 10log
l
?? 
  In case of point source, 
2
21
2
12
lr 1
l or
r l r
??
??
??
??
 
  In case of line source, 
21
12
lr 1
l or
r l r
??
??
??
??
 
4.  Doppler Effect In Sound 
     
m0
ms
v v v
f ' f
v v v
?? ??
?
??
??
??
 
5. Beats 
   f
b
= f
1
 - f
2
 (f
1
 > f
2
) 
6.  Oscillations of Stretched Wire or Organ Pipes  
  (i) Open organ pipe 
  Fundamental tone or first harmonic (n = 1) 
 
  First overtone or second harmonic (n = 2) 
 
  Second overtone or third harmonic (n = 3) 
 
   
v
fn
2l
??
?
??
??
. Here, n = 1,2, 3...... 
  Even and odd both harmonics are obtained. Here, v = speed of sound in air. 
  v will be either given in the question, otherwise calculate from 
RT
v
M
?
? 
  (ii) Closed organ pipe 
  Fundamental tone or first harmonic (n = 1) 
Page 3


Important Formulae 
1.  Wave Speed 
  Speed of longitudinal wave 
     
E
v ?
?
 
  (a) In solids, E = Y = Young's modulus of elasticity 
     
Y
v ?
?
 
  (b) In liquids, E = B = Bulk modulus of elasticity 
     
B
v ?
?
 
  (c) In gases, according to Newton, 
   E = B
T
 = Isothermal bulk modulus of elasticity = p 
   
p
v ?
?
 
  But results did not match with this formula. Laplace made correction in it. According to him, 
  E = B
S
 = Adiabatic bulk modulus of elasticity = ? ? 
     
p RT kT
v
Mm
? ? ?
? ? ?
?
 
2.  Effect of Temperature, Pressure and Relative Humidity in Speed of Sound in Air (or in a Gas) 
  (i) With temperature v ? T 
(ii) With pressure Pressure has no effect on speed of sound as long as temperature remains 
constant.  
(iii) With relative humidity With increase in relative humidity in air, density decreases. Hence, 
speed of sound increases. 
3.  Sound Level (L) 
   
10
0
l
L 10log
l
? (in dB) 
Here, I
0
 = intensity of minimum audible sound = 10
-12
 W m
-2
. While comparing loudness of two 
sounds we may write, 
   
2
2 1 10
1
l
L L 10log
l
?? 
  In case of point source, 
2
21
2
12
lr 1
l or
r l r
??
??
??
??
 
  In case of line source, 
21
12
lr 1
l or
r l r
??
??
??
??
 
4.  Doppler Effect In Sound 
     
m0
ms
v v v
f ' f
v v v
?? ??
?
??
??
??
 
5. Beats 
   f
b
= f
1
 - f
2
 (f
1
 > f
2
) 
6.  Oscillations of Stretched Wire or Organ Pipes  
  (i) Open organ pipe 
  Fundamental tone or first harmonic (n = 1) 
 
  First overtone or second harmonic (n = 2) 
 
  Second overtone or third harmonic (n = 3) 
 
   
v
fn
2l
??
?
??
??
. Here, n = 1,2, 3...... 
  Even and odd both harmonics are obtained. Here, v = speed of sound in air. 
  v will be either given in the question, otherwise calculate from 
RT
v
M
?
? 
  (ii) Closed organ pipe 
  Fundamental tone or first harmonic (n = 1) 
 
  First overtone or third harmonic (n = 3) 
 
  Second overtone or fifth harmonic (n = 5) 
 
  
v
fn
4l
??
?
??
??
 . Here, n = 1,3,5......  
(a) Stationary transverse waves are formed in stretched wire and longitudinal stationary waves are 
formed in organ pipes. 
(b) Open end of pipe is displacement antinode, but pressure and density nodes. Closed end of pipe 
is displacement node, but pressure and density antinodes. 
  (c) Laplace correction e =0.6r (in closed pipe) and 2e = 12 r (in open pipe) 
  Hence, 
v
fn
2(l 12r)
??
?
??
?
??
 (in open pipe) and 
v
fn
4(l 0.6r)
??
?
??
?
??
 (in closed pipe) 
(iii) If an open pipe and a closed pipe are of same lengths then fundamental frequency of open 
pipe is two times the fundamental frequency of closed pipe. 
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