• Pitch or Shrillness:-Pitch is a sensation which determines the shrillness of sound. It is subjective and cannot be measured quantitatively. It depends up on frequency and relative motion
between the sources and the listener.
• Quality or Timber:- It is that characteristic of a musical sound which enables us to distinguish between two notes of the same pitch and loudness produced by two different sources.
• Velocity u of longitudinal wave (sound) [Newton’s Formula]:-
u = √E/ρ
Here E is the coefficient of elasticity and ρ is the density of medium.
• Velocity of sound in solids:-
u = √Y/ρ
Here Y is the young’s modulus of elasticity and ρ is the density.
• Velocity of sound in liquids:-
u = √B/ρ
Here B is the Bulk modulus of elasticity and ρ is the density.
• Velocity of sound in gases:-
u = √γP/ρ
Here, γ (=cP/cV) is the adiabatic ratio, P is the pressure and ρ is the density.
• Various factors affecting velocity of sound:-
(a) Effect of density:- The velocity of sound in a gas varies inversely as the square root of its
density. u1/ u2 = √*ρ2/ρ1]
(b) Effect of moisture:-um/ud= √*ρd/ ρm]
Since, ρm<ρd, then, um>ud
This signifies sound travels faster in moist air.
(c) Effect of pressure:- u=√γP/ρ=√γk = constant
This signifies, change of pressure has no effect on the velocity of sound.
(d) Effect of temperature:- ut/u0 =√ρ0/ρt= √T/T0
Thus, velocity of sound varies directly as the square root temperature on Kelvin’s scale.
(e) Temperature coefficient of velocity of sound (α):- α = u0/546 = (ut-u0)/t
• Overtones in open pipe:-An open pipeis open at both ends. Since air is free to vibrate at an open end, we must get an antinode at the open end
(a) Fundamental frequency:-
Wavelength, λ=2l
Frequency, f=u/2l = (1/2l)√(γP/ρ)
Here l is the length of the pipe and u is the velocity of sound.
(b) First overtone (Second Harmonic):-
Wavelength, λ1=l
Frequency, f1=2f
c) Second overtone (Third Harmonic):-
Wavelength, λ2=2l/3
Wavelength, f2=3f
• Overtones in closed pipe:-Since air, at a closed end, is not free to vibrate, there must be a node at a closed end always.
(a) Fundamental frequency:-
Wavelength, λ=4l
Frequency, F=u/4l = (1/4l)√(γP/ρ)
Here l is the length of the pipe and u is the velocity of sound.
(b) First overtone (Third Harmonic):-
Wavelength, λ1=(4/3)l
Frequency, F1=3F
(c) Second overtone (Fifth Harmonic):-
λ2 = 4l/5
F2 = 5F
• Comparison of fundamental frequencies of a closed end of an open pipe:- f = 2F
• Doppler’s Effect:-Theapparent change in pitch of a note, due to the relative motion between the source and the listener is called Doppler’s effect.
(a) Source in motion, listener at rest:-
(i) Source approaching the listener:-
Modifying wave length, λ' = V-a/f
Apparent frequency, f' = [V/V-a]f
Change in frequency, ?f = (a/V-a)f
Here V is the velocity of sound in air and a is the velocity of source when it moves towards the listener.
(ii) Source going away from the listener:-
Apparent frequency, f' = [V/V+a]f
Change in frequency, ?f = -(a/V+a)f
(iii) Source crossing the listener:-
Apparent frequency of the source before crossing = (V/V-a) f
Apparent frequency of the source after crossing = (V/V+a) f
Change in frequency, ?f = -(2aV/V2-a2)f
(b) Source at rest, listener in motion:-
(i) Listener moving away from source:-
Apparent frequency, f'= [V-b/V]f
Change in frequency, ?f = (-b/V)f
Here b is the velocity of listener.
(ii) Listener moving towards the source:-
Apparent frequency:-f'= [V+b/V]f
Change in frequency, ?f = (+b/V)f
(iii) Listener crossing the source:-
Apparent frequency of the source before crossing = (V+b/V) f
Apparent frequency of the source after crossing = (V-b/V) f
Change in frequency, ?f =-2fb/V
