2. Sound
Has speed of about 332 ms-1 in air and 1500
ms-1 in water and up to 500 ms-1 in steel. It
varies with temperature of transmitting
medium
Properties
Reflection (echo)
Speed of sound heard by a listener after an
echo v = 2x/t
Use: To calculate the depth of the sea by
sonar
x = vt/2
3. Beat and apparent frequency
Beat: When 2 notes of nearly equal
frequency are sounded together
f = f1 – f2
Apparent frequency: A phenomenom
associated with moving sound.
Doppler effect is change in frequency (pitch)
of a source when there is a relative motion
between the source and observer. When
sound moves further away the observer
tends to hear a drop in the pitch.
4. Source and observer stationary
λ = v/f
Source moving, observer stationary
λ’ = v – vs
f
Apparent frequency f’ = v/λ’
S
V
O
S
Vs
O
v = (v –vs)
5. f’ = v f’ = ( v ) x f *f=real frequency
(v – vs) v - vs
f
O approaching stationary S
v = v + v0
v0 = velocity of observer
f’ = v/λ’S O
v0
6. f’ = v + v0 (v + v0) x f
v/f v
If O and S are moving in the saame direction
f’ = (v + v0 ) x f
(v – v0 )
7. Eg
An ambulance emitting siren sounds at 440
Hz is moving at a velocity of 50ms-1
What is the apparent frequency as it
approaches a stationary observer?
(speed of wave = 331 ms-1 )
8. f’ = f’ = ( v ) x f
(v – vs)
= 331 x 440 = 518 Hz
331 - 50
10. Vibrations in a closed pipe:
frequencies and harmonics
l = λ/4 λ = 4l
f0 = v/λ = v/4l *fundamental f of a closed pipe
f1 at l2 l2 = 3λ/4 λ = 4l/3
f = v = 3v/4l
4l/3
• Remember f0 = v/4l
= 3 x v/4l = 3fo
Harmonics = 3f0, 5f0, 7f0, ...
only odd harmonics are possible
12. Vibrations in an open pipe:
frequencies and harmonics
f0 at l1= v/λ l1 = λ/4 λ = 2l
f0 = v/2l
f1 at l2= v/λ = v/l = 2v/2l = 2f0
f2 at l3 = v/λ λ = 2l/3
f2 = 3v/l = 3f0
Harmonics = f0, 2f0, 3f0, 4f0, ....
All harmonis are possible
13. Remember
Velocity of a wave propagated along a fixed
wire or string
v = √T/m
T = Tension in the string
m = mass per unit lenght of the string
f0 = 1/2l √T/m
