Class 11th Physics - Waves Case Study Questions and Answers 2022 - 2023
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Waves Case Study Questions With Answer Key
11th Standard CBSE
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Reg.No. :
Physics
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A wave motion is a means of transferring energy and momentum from one point to another without any actual transportation of matter between these points. In wave motion, disturbance travels through some medium but medium does not travel along with the disturbance. For propagation of wave, medium must possess two essential property viz. inertia and elasticity. Disturbance produced at one point is communicated to the adjoining particle which also start vibrating simple harmonically about their mean positions. Hence the wave motion travels on and on. Wave motion is categorised as longitudinal and transverse on the basis of mode of vibration of particles of medium.
(i) What are elastic waves?
(ii) Explain two types of wave motion.
(iii) Mention the characteristic of medium in which longitudinal and transverse waves propagate.
(iv) What are compression and rarefaction in a longitudinal wave propagation?
(v) Why are longitudinal waves called pressure waves?
(vi) What type of waves are the sound and the light waves?
(vii) An explosion occurs inside a lake. What type of waves are produced inside the water?(a) -
Sound travels through a gas in the form of compressions and rarefactions. Newton assumed that the changes in pressure and volume of gas, when sound waves are propagated through it, are isothermal. The amount of heat produced during compression, is lost to the surrounding and similarly the amount of heat lost during rarefaction is gained from the surroundings. So as to keep the isothermal elasticity. Laplace, a french mathematician pointed out that Newton's assumption was wrong. According to Laplace, the changes in pressure and volume of a gas, when sound waves propagated through it, are not isothermal but adiabatic.
(i) Write the Newton's formula for velocity of sound in gases and Laplace correction in it.
(ii) What is the effect of pressure on velocity of sound in gases?
(iii) Find the ratio of velocity of sound in Hydrogen and Oxygen.
(iv) Define temperature coefficient of velocity of sound in air.
(v) What is effect of humidity on the speed of sound in air?
(vi) Explain why propagation of sound in air is an adiabatic process?
(vii) If tension of a wire is increased to four times, how is the wave speed changed?(a) -
The principle of super position of waves enables us to determine the net waveform when any number of individual waveforms overlap. The net displacement at a given time is the algebraic sum of the displacements due to each wave at that time. When two sets of progressive wave trains of the same type having the same amplitude and same time period travelling with the same speed along the same straight line in opposite directions superimpose a new set of waves are formed. These are called strationary waves or standing waves. The resultant waves do not propagate in any direction, nor there is any transfer of energy in the medium. In stationary waves, there are nodes and anti nodes point where particles are at rest and have largest amplitude respectively.
(i) How amplitude of vibration vary in stationary wave?
(ii) What is energy of stationary wave?
(iii) What is distance between consecutive node, antinode and between node and antinode?
(iv) What is phase difference between particles vibrating in a segment of stationary wave and between adjoining segments?
(v) Why is a stationary wave so named?
(vi) Where will a person hear maximum sound, at node or antinode?
(vii) Name the type of stationary wave produced by an organ pipe, open at both ends.(a) -
When two sound waves of-nearly same frequency and amplitudes travelling in a medium along the same direction, super-impose on each other, then the intensity of the resultant sound at a particular position rises and falls alternately with time. This phenomenon is known as beat. if intensity of sound is maximum at time t = 0, one beat is said to be formed when intensity becomes maximum again, after becoming minimum once in between. The time interval between two successive beats is called beat period. The number of beats produced per second is called beat frequency.
(i) Two sound waves of frequency v1 and v2 superimpose to form beats. What is the beat frequency?
(ii) What should be the difference in frequency of two sound waves to form beats? Give reason
(iii) Write two applications of the phenomenon of beats.
(iv) Two sounds of very close fequencies, say 256 Hz and 260 Hz are produced simultaneously. What is the frequency of resultant sound and also write the number of beats heard in one second?
(v) A sitar wire and a tabla, when sounded together, produce 5 beats per second. What can be concluded from this? If the tabla membrane is tightened will the beat rate increase or decrease?
(vi) A tuning fork of unknown frequency gives 4 beats with a tuning fork of frequency 310 Hz. It gives the same number of beats on filing. Find the unknown frequency.(a) -
Whenever there is a relative motion between the source of sound, the observer and the medium, the frequency of sound as received by the observer is different from the frequency of sound emitted by the source. For example to a man standing on a railway platform, when a train blowing its whistle, approaches him, the pitch of the whistle appears to rise and it suddenly appears to drop as the engine moves away from him. Similar effect is observed when the source is at rest and observer moves towards or away from the source. This phenomenon is noticeable only when the relative velocity between the source and the observer is an appreciable fraction of the wave velocity.
(i) Name the phenomenon observed in the passage. Define it.
(ii) On what factors does the apparent frequency of sound depends?
(iii) What physical change occurs when a source of sound moves and the listener is stationary?
(iv) What physical change occurs when the source of sound is stationary but the listener moves?
(v) A particle travelling with a speed of 0.9 of the speed of sound and is emitting radiations of frquency of 1 KHz and moving towards the observer. What is the apparent frequency of radiation?
(vi) Write the condition in doppler effect when apparent frequency of sound increases.
(vii) Write two applications of Doppler effect.(a)
Case Study
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Answers
Waves Case Study Questions With Answer Key Answer Keys
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(i) Waves which can be produced or propagated only in a material medium having properties of elasticity and inertia, are known as elastic waves or mechanical waves.
(ii) Transverse wave motion: When the particles of the medium vibrate about their mean position in a direction perpendicular to the direction of propagation of disturbance.
Longitudinal wave motion: When the particles of the medium vibrate about their mean position in the direction of propagation of disturbance.
(iii) The propagation of longitudinal waves through medium requires that medium should possess bulk modulus of elasticity. While transverse waves can propagate only in the medium, which possess shear modulus of elasticity.
(iv) Compression is a region of the medium, in which particles come to distance less than the normal distances between them.
Rarefaction is a region of the medium, in which particles of the medium get apart to distances greater than the normal distances between them.
(v) This is because propagation of longitudinal waves through a medium involves changes in pressure and volume of air, when compression and rarefactions are formed.
(vi) Sound waves are longitudinal in nature and light waves are transverse in nature.
(vii) Longitudinal waves. It is because, a liquid possess volume elasticity. The modulus of rigidity is practically zero for liquids. -
(i) Newton's formula for velocity of sound in gases \(v=\sqrt{\frac{\mathrm{B}}{\rho}}=\sqrt{\frac{P}{\rho}}\) where B is bulk modulus and \(\rho\) density of gas. It is based on assumption that propagation is isothermal process. While Laplace correction is that propagation of sound in air is adiabatic process.
\(v=\sqrt{\frac{\gamma P}{\rho}}\)
(ii) Velocity of sound is independent of the change in pressure of the gas, provided temperature remains constant.
(iii) \(\frac{V_{H}}{v_{0}}=\sqrt{\frac{\rho_{0}}{\rho_{\mathrm{H}}}}=\sqrt{\frac{16 \rho_{H}}{\rho_{H}}}=4: 1\)
(iv) It is change in the velocity of sound when temperature changes by 1°C rise in temperature.
(v) Density of air is inversely proportional to humidity i.e., humid air is less dense than dry air. Therefore velocity of sound in moist air is greater than the velocity of sound in dry air as velocity is inversely proportional to density of air.
(vi) It is due to following two reasons
(i) Velocity of sound in gas is large therefore there is no time left for any exchange of heat amongst compression and rarefaction.
(ii) A gas is bad conductor of heat. It does not allow the free exchange of heat between compressed layer, rarefied layer and surroundings.
(vii) As \(v \propto \sqrt{T}\) therefore wave speed becomes twice. -
(i) Amplitude of vibration of particles from zero at nodes to maximum at antinodes
(ii) The total energy associated with a stationary wave is twice the energy of each of incident and reflected wave.
(iii) Two consecutive nodes or anti nodes are separated by a distance \(\frac{\lambda}{2}\) distance between a node and adjoining anti-node is \(\frac{\lambda}{4} \text { . }\)
(iv) All particles in one particular segment vibrate in the same phase while particles in the consecutive segments differ in phase by 180o.
(v) This is because is a stationary wave, disturbance is not propagated. It is confined in a particular region.
(vi) Perception of sound is due to pressure variations - which is maximum at nodes.
(vii) An organ pipe, open at both ends produces Longitudinal stationary waves. -
(i) Beat frequency is equal to difference of frequency between two waves. i.e., n = v1 - v2 .
(ii) For the formation of distinct beats, frequencies of two sources of sound should be less than 10. It is because impression of a sound heard by our ears persists on our mind for \(\frac{1}{10} \mathrm{th}\) of a second. In order to hear distinct beats, time interval between two successive beats must be greater than \(\frac{1}{10} \) second.
(iii) Two important application of the phenomenon of beats are
(i) It is used in the determination of unknown frequencies.
(ii) It is used in detecting the presence of dangerous gases in mines.
(iv) Frequency of resultant sound
\(v_{a v}=\frac{v_{1}+v_{2}}{2}=\frac{256+260}{2}=258 \mathrm{~Hz}\)
Number of beats heard in one second = 260 - 256 = 4
(v) f the tabla membrane is tightened i.e., tension is increased, the frequency (v2 ) of the sound produced by the tabla will increase. If v1 (frequency of sitar) > v2 ' the beat frequency will decrease and if v1 < v2 the beat frequency will increase.
(vi) Unknown frequency = known frequency ± beat frequency = 310 ± 4 = 314 or 306 Hz. As frequency increases on filing, therefore initial unknown frequency = 306 Hz. -
(i) It is Doppler effect. According to this, there will be the apparent change in the frequency of sound when the source, the observer and the medium are in relative motion.
(ii) Apparent frequency of sound depends on three factors
(i) velocity of source
(ii) velocity of the observer and
(iii) velocity of the medium or wind.
(iii) Wavelength of sound waves changes.
(iv) The number of sound waves received by the listener changes.
(v) Apparent Frequency
\(v^{\prime}=\left(\frac{v}{v-v_{s}}\right) v=\frac{v}{v-0.9 v} \times 1 \mathrm{KHz}\)
= 10 kHz
(vi) Apparent frequency of sound increases when source moves towards listener or listener moves towards source or both move towards each other.
Change in frequency or Doppler shift is used
(i) in the military to detect the enemy aircraft.
(ii) by the astrophysicists to measure the velocities of planets and stars.
Case Study
