Stationary Wave: Short Questions and Numericals

Short Answer Questions:                                                                                                                             AP

1.       How are stationary waves formed?

2.       Longitudinal waves cannot be polarized. Why?

3.       A radio station broad casts at 800Khz. What will be the wavelength of the wave?

4.       Why longitudinal wave propagate in liquid?

5.       What is progressive wave? Give example.

6.       What do you mean by resonance?

7.       Can transverse wave be produced in air?

8.       If you set your watch by the sound of distant siren, will it go fast or slow?

9.       A wave transmits energy. Does it transfer linear momentum?

10.   Energy can be transferred by particles as well as by waves. How can we distinguish experimentally between these two methods of energy transfer?

11.   Bells are made up of wood but not of wood. Why?

12.   We prefer knocking rather than calling someone inside a closed room. Why?

13.   What do you mean by reflection, refraction, diffraction, interference and polarization of sound?

14.   Can sound waves be polarized?

15.   How the energy transmits during transmission of waves?

16.   Why do stages of large auditorium have curved backs?

17.   Why is diver under water unable to hear sounds produced in air?

18.   What are the main differences between light waves and sound waves?

19.   Velocity of sound waves increased in a cloudy day. Why?

20.   Sound made at a distance can be heard distinctly at night than in day(or wet day than on a dry day)?

21.   What is the drawback of Newton’s formula for the velocity of sound?

22.   What was the necessity to introduce Laplace’s correction in velocity of sound?

23.   Why does empty vessel sound more than a filled one?

24.   Change in pressure does not affect the velocity of sound. Explain?

25.   Do sound waves need a medium to travel from one point to another point in space? What properties of the material are relevant?

26.   Does the velocity of sound depends on the atomicity of the gas?

27.   Does the sound of an explosion faster than the sound produced by a humming bee?

28.   What are the properties of medium for the propagation of a mechanical wave?

29.   Why do we hear more clearly in a curtained room than in a non-curtained room?

30.   Velocity of sound is greater in hydrogen than that in oxygen. Why?

31.   Show that when temperature of air (gas) changes by 1⁰C, the velocity of sound passing through it changes by 0.61ms^-1.

32.   Explain the term disturbance with examples?

33.   Explain the phenomenon of superposition? How constructive and destructive interference is produced?

AP

Interference of waves

When two or more waves combine at a particular point, they are said to interfere, and the phenomenon is called interference. More precisely,

The interference is the phenomena of superposition of two waves of same frequency travelling in the same direction.

Due to interference of waves, the resultant wave is of higher amplitude or lower amplitude depending upon the phase of propagation of waves. If two waves propagating in same direction interfere and are in phase with each other the resultant amplitude will be the sum of amplitude of both waves and is known as constructive interference. And if two waves propagating in same direction interfere and are out of phase or are in opposite phase than the resultant amplitude will be the difference of their amplitudes and is known as destructive interference.

If y₁=A₁sin(wt-kx) and y₂ = A₂ sin(wt-kx+φ) are two waves of same frequency and of arbitrary amplitude travelling in same direction and φ is the phase difference between them, when the interference occurs between them then by the superposition principle we get resultant amplitude as

R = (A₁² + A₂² + 2A₁A₂cosφ)^1/2

The resultant amplitude R has maximum value for cosφ = 1 and minimum value for cosφ = -1

R = A₁ + A₂  is the amplitude of constructive interference and

R = A₁ – A₂is the amplitude of destructive interference.

Resultant wave
Wave 1
Wave 2
	Constructive interference	Destructive interference

Fig: constructive and destructive interference.

Reflection of Waves

Just as the light waves or rays get reflected from the plane surface such as mirror sound waves also gets reflected. Reflection of wave also follows the laws of reflection of light.

In fig S is a source for sound waves, which are reflected at point N on smooth surface AB, guided by material T₁ , the maximum intensity of sound is detected at R and we can say that,

               

SNN₁  =   RNN₁                                   i.e.      i=    r

Similarly it can be shown that sound wave can be focused by a curved concave smooth surface. A parabolic surface is used to transmit and receive waves to or from a long distances (parabolic or disc antennas)  by placing a source or a receiver at the focus and it is widely used in communication systems.

All of us had heard echo from a solid wall. It is an example of sound waves.

Refraction of Wave:

Refraction is the bending of waves when they enter a medium where their speed is different.

The understanding of refraction of sound wave explain why it is easier to hear at night than during a day time. During day time the upper layers are colder and therefore heavier than the layer near earth surface. Sound moves faster in a medium with higher temperature and slower in cold air. In analogy with light refraction the faster moving waves in hot air bend away from the boundary towards the normal when they encounter cold air. Therefore, the sound waves are refracted in the direction away from the earth. The intensity of the sound wave diminishes. At night time, however, the layers of air near earth’s surface are colder than those higher up, and hence sound waves are now refracted towards the earth, with a consequent increase in intensity.

Diffraction of waves:

The phenomenon of spreading of waves when they pass through apertures or around obstacles is known as diffraction. For the phenomena of diffraction to be observed, the width of the aperture or obstacle must be comparable to the wavelength of waves.

Polarization of waves:

The phenomenon which explains the nature of particle motion of a wave, is polarization. It is observed only for transverse waves. A light wave being transverse shows polarization. Sound wave does not shows polarization effect because it is a longitudinal wave and particles vibrate about their mean position only in one direction-along the direction of propagation.

                                                                                                                               

                                                                                                                                                                                                  AP

Numerical problems:

1.       Calculate the change in wavelength of sound wave of frequency 1000 Hz when it enters into water from air. V_air=344 ms^-1 ,V_water=1480ms^-1                                                    Ans1.136m

2.       A man standing at one end of a closed corridor 57m long blow a short blast on a whistle. He found that the time from the blast to the sixth echo was 2s. if the temperature was 17⁰C. What was the velocity of sound at 0^oC?                                                                      Ans: 331.8ms^-1

3.       Calculate the temperature at which the sound travels in hydrogen with the same speed as in helium at NTP. The density of helium is twice that of hydrogen.                        Ans: -136.5⁰C

4.       When a detonator exploded on a railway line, an observer standing on the rail 2Km away hears two sounds. What is the time interval between them? Y_steel= 2×10¹¹ Nm^-2 , density of steel = 8000 kgm^-3density of air=1.4, ϒ-for air=1.4, atmospheric pressure = 10⁵Nm^-2.                             Ans: 5.925s

5.       The velocity of sound in air saturated with water vapor at 30⁰C is 340m/s. if the atmospheric pressure is 65cm of Hg and s.v.p. of water at 30⁰Cis 31.7mm of Hg. Calculate velocity of sound in dry air at 0⁰C.                                                                                                                                  Ans: 319.74m/s

6.       Calculate the value of ϒ for a gas where adiabatic bulk modulus of elasticity is 1.43×10⁵Nm^-2. If the density of gas is 1.55 Kgm^-3, calculate the velocity of sound through the gas. Ans:1.41, 303.74

7.       A steel pipe 100m long is struck at one end and a person hears to sound at the other end. One sound reaches the ear through air and the other reaches it through the steel. The density of steel is 7500 kgm^-3 that of air at STP is 1.293kgm^-3. If the young modulus of steel is 2×10¹¹Nm^-2. Find the time interval between two sounds. ϒ=1.4.                                                       Ans: 0.282s

8.       If the amplitudes of the two waves are 3 units and 1 units respectively, show by the principle of superposition that the ratio of the amplitudes of the stationary wave at an antinode and node respectively is 2:1.

9.       The speed of sound in water is 1480ms^-1. Find the frequency of sound wave such that it’s wavelength in water is the same as the wavelength of another sound wave of frequency 1 khz in air at 20⁰C. Velocity of sound at NTP=332ms^-1.                                                    4.302KHz

10.   A steel wire stretched with a tension 50N. what is its mass per unit length if the speed of transverse waves on the wire is same as the speed of sound in air at 0⁰C.                                0.422×10^-3kg/m

11.   A stone is dropped into a well of 78.4m deep. After what time will the splash of water be heard. Velocity of sound in air = 340 ms^-1.                                                                                4.224s