Upload
britton-blake
View
216
Download
0
Embed Size (px)
Citation preview
Physics
Wave and Sound - 2
Session
Session Objectives
Session Objective
1. Nature and propagation of sound waves
2. Displacement and pressure wave
3. Reflection & Transmission of Waves
4. Linear Wave Equation (Differential Form)
5. Superposition & Interference of Sinusoidal
Waves
6. Speed of Sound Waves in a material and
Laplace correction
Longitudinal waves
Produced by a Vibrating Source
Elasticity and Inertia are necessary
Nature and propagation of sound waves
Propagates Through-
• Compression
Rarefaction
Audible Range: 20 to 20000 Hz
Ultrasonic Range: > 20000 Hz
Infrasonic Range: < 20 Hz
Displacement and pressure wave
BA xP cos t
v v
0
B AP BkA
v
The displacement wave is given by
y A sin t kx
The pressure waves is given by
where
Displacement and pressure wave
Pressure wave and displacement wave
have a phase difference of , i.e.
pressure maxima occurs where
displacement is zero and displacement
maxima occurs where the pressure is at
its normal level.
2
Reflection & Transmission of Waves
Sound wave undergoes a phase change of 180o on reflection from a rigid boundary compared to incident wave
Linear Wave Equation (Differential Form)
2 2
2 2 2
d y 1 d y
dx v dt
The above equation represents a progressive wave.
Any function that satisfies the above equation
represents a progressive wave
•Two or more waves having constant phase difference meet in the same medium
y = y1+y2 = f1(x-vt)+f2(x-vt+ )
y1 and y2 must be specific to find f
Interference
Superposition and Interference of sinusoidal Waves
1 1
2 2
Y A sin t kx
Y A sin t kx
1 2Y Y Y A sin t kx
2 21 2 1 2A = A + A +2A A cosφ -1 2
1 2
A sinφδ = tan
A + A cosφ
2m ax 1 22n I ( I I ) maxima
2m in 1 2(2n 1) I ( I I ) [minima]
Constructive
Destructive
Types of interference
1 2 1 2
x n
I I I 2 I I
1 2 1 2
1x (n )
2
I I I 2 I I
Young’s Double Slit Experiment
In general : Elastic Propertyv =
Inertial Property
In a fluid medium
( density) B
v =ρ
(Y Young'smodulus)In a solid rod : Y
v
Speed of sound in gases = v = P
Speed of Sound Waves in a material and Laplace correction
Class Test
Class Exercise - 1
Two waves represented by and
are superimposed. The
resultant waves will have an amplitude
(a) a (b)
(c) 2a (d) 0
y acos kx t y asin kx t
2a
Two waves have phase difference
2
2 2 2 2A a a 2a cos
2 A 2a
Solution :
Hence answer is (b).
Class Exercise - 2
A propagating sound wave encounters
rigid boundary. The reflected wave will
have the phase difference of
(a) (b)
2
(c) 0 (d) none of these
When sound wave encounters rigid
boundary, there is change in phase by .
Solution :
Hence answer is (b).
Class Exercise - 3
If there are two drum-beaters beating
the drums independently, the
sources would be
(a) coherent
(b) Incoherent
(c) Cannot be determined
(d) Data insufficient
In this case, the frequency difference is constant.
Solution :
Hence answer is (a).
Class Exercise - 4
The velocity of sound wave in a solid does
not depend on
(a) Young’s modulus (b) density
(c) conductivity (d) None of these
Velocity does not depend on conductivity.
Hence answer is (c).
Solution :
Class Exercise - 5
Consider the following statements about
sound passing through a gas.
A : The pressure of the gas at a point
oscillates in time.
B : The position of a small layer of the gas
oscillates in time.
(a) Both A and B are correct (b) A is correct but B is wrong
(c) B is correct but A is wrong (d) Both A and B are wrong
Sound wave is longitudinal wave. Hence, both pressure
and position oscillate with time.
Hence answer is (a).
Solution :
Class Exercise - 6
When we clap our hands, the sound
produced is best described by
0 0
0 n n n
(a) P P sin(kx t) (b) P P coskx sin t
(c) P P sina cos t (d) P Po sin k x t
Sound produced is the mixture of
various sound waves.Hence answer is (d).
Solution :
Class Exercise - 7
The equation of a sound wave in air is
given by
. The speed of sound in air is given by
(a) 330 m/s (b) 335 m/s
(c) 325 m/s (d) None of these
2 1 1P 0.01 N/m sin 1000 s t 3m x
3
v
1000
v 330 m/s3 3
Hence answer is (a).
Solution :
Class Exercise - 8
Two waves reach a point with a path
difference of 12 cm. The waves have
wavelength 4 cm. The phase difference
of two waves is
(a) 6 (b) 3
2(c) (d)
3 3
Hence answer is (a).
Solution :
212 6
4
Phase difference = Path difference × 2
Class Exercise - 9
A wave of frequency 4.5 MHz has a speed
of 1.5 km/s in a material. The wavelength
of wave in this material is
(a) 3.3 × 10–4 m (b) 3.3 × 10–3 m
(c) 3.3 × 10–7 m (d) 3.3 × 10–9 m
Solution
Hence answer is (a).
Frequency f = 4.5 × 106 Hz
Velocity v = 1.5 km/s = 1500 m/s
46
v 15007.6 10 m
f 4.5 10Wave length
Class Exercise - 10
Two point sources of sound are kept at
a separation of 10 cm. They vibrate in
phase to produce waves of wavelength
5 cm. What would be the phase
difference between the two waves
arriving at a point 20 cm from one
source on the line joining the sources?
Solution
Hence answer is (a).
Path difference between waves
coming source S1 and S2 = 30 – 20 =
10 cm.
Hence, phase difference
210 4
5
S1
S2
10
20
D
Thank you