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 Hz Ultrasonic Range: > Hz Infrasonic Range: < 20 Hz

Displacement and pressure wave The displacement wave is given by 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.

Reflection & Transmission of Waves Sound wave undergoes a phase change of 180 o on reflection from a rigid boundary compared to incident wave

Linear Wave Equation (Differential Form) 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 = y 1 +y 2 = f 1 (x-vt)+f 2 (x-vt+ ) y 1 and y 2 must be specific to find f Interference

Superposition and Interference of sinusoidal Waves

 Constructive  Destructive Types of interference

Young’s Double Slit Experiment

In general : In a fluid medium In a solid rod : Speed of sound in gases = v = 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 Two waves have phase difference Solution : Hence answer is (b).

Class Exercise - 2 A propagating sound wave encounters rigid boundary. The reflected wave will have the phase difference of 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 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 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 Hence answer is (a). Solution : Phase difference = Path difference ×

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 × 10 6 Hz Velocity v = 1.5 km/s = 1500 m/s Wave 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 S 1 and S 2 = 30 – 20 = 10 cm. Hence, phase difference

Thank you