344
8 Waves
(b) Source is At Rest, Observer in Motion
Let the observer be moving with speed v 0 . Then
f
= f
(v ± v 0 )
v
(8.30)
where the plus sign is for motion towards the source and the minus sign for motion
away from the source.
(c) Both Source and Observer in Motion
f
= f
(v ± v 0 )
(v ∓ v s )
(8.31)
(d) If the medium moves with velocity W relative to the ground along the line joining source and observer,
f
= f
(v + W ± v 0 )
(v + W ∓ v s )
(8.32)
Shock waves are emitted when the observer’s velocity or the source velocity
exceeds the sound velocity and Doppler’s formulae break down. The wave front
assumes the shape of a cone with the moving body at the apex. The surface of the
cone makes an angle with the line of flight of the source such that
sin θ = v/v s
(8.33)
The ratio v s /v is called Mach number. An example of shock waves is the wave
resulting from a bow boat speeding on water, a second example is a jet-plane or
missile moving at the supersonic speed, a third example is the emission of Cerenkov
radiation when a charged particle moves through a transparent medium with a speed
exceeding that of the phase velocity of light in that medium.
Echo is defined as direct reflection of short duration sound from the surface of a
large area. If d is the distance of the reflector, V the speed of sound then the time
interval between the direct and reflected waves is
T = 2d/v
(8.34)
Reverberation: A sound once produced in a room will get reflected repeatedly from
the walls and become so feeble that it will not be heard. The time t taken for the
steady intensity level to reach the inaudible level is called the time of reverberation:
T R = 0.16V /K S
(Sabine law)
(8.35)
8 Waves
(b) Source is At Rest, Observer in Motion
Let the observer be moving with speed v 0 . Then
f
= f
(v ± v 0 )
v
(8.30)
where the plus sign is for motion towards the source and the minus sign for motion
away from the source.
(c) Both Source and Observer in Motion
f
= f
(v ± v 0 )
(v ∓ v s )
(8.31)
(d) If the medium moves with velocity W relative to the ground along the line joining source and observer,
f
= f
(v + W ± v 0 )
(v + W ∓ v s )
(8.32)
Shock waves are emitted when the observer’s velocity or the source velocity
exceeds the sound velocity and Doppler’s formulae break down. The wave front
assumes the shape of a cone with the moving body at the apex. The surface of the
cone makes an angle with the line of flight of the source such that
sin θ = v/v s
(8.33)
The ratio v s /v is called Mach number. An example of shock waves is the wave
resulting from a bow boat speeding on water, a second example is a jet-plane or
missile moving at the supersonic speed, a third example is the emission of Cerenkov
radiation when a charged particle moves through a transparent medium with a speed
exceeding that of the phase velocity of light in that medium.
Echo is defined as direct reflection of short duration sound from the surface of a
large area. If d is the distance of the reflector, V the speed of sound then the time
interval between the direct and reflected waves is
T = 2d/v
(8.34)
Reverberation: A sound once produced in a room will get reflected repeatedly from
the walls and become so feeble that it will not be heard. The time t taken for the
steady intensity level to reach the inaudible level is called the time of reverberation:
T R = 0.16V /K S
(Sabine law)
(8.35)