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Waves Physics - Waves

UP Board (UPMSP) - STD 11 Science - Physics (UPMSP - English Medium). 466 questions in this chapter.

Question types

Waves question types

466 questions across 7 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.

466
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7
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5
Question types
Sample Questions

Waves questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
A train whistling at constant frequency is moving towards a station at a constant speed $V.$ The train goes past a stationary observer on the station. The frequency $n′$ of the sound as heard by the observer is plotted as a function of time $t$ Identify the expected curve:
  • A
    Image
     
  • B
    Image
  • ✓
    Image
     
  • D
    Image

Answer: C.

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Q 2M.C.Q (1 Marks)1 Mark
During propagation of a plane progressive mechanical wave:
  • A
    All the particles are vibrating in the same phase.
  • B
    Amplitude of all the particles is equal.
  • C
    Particles of the medium executes $\text{S.H.M.}$
  • ✓
    All of the above

Answer: D.

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Q 3M.C.Q (1 Marks)1 Mark
Two sine waves travel in the same direction in a medium. The amplitude of each wave is a and the phase difference between the two waves is $120^\circ.$ The resultant amplitude will be:
  • ✓
    $A$
  • B
    $2A$
  • C
    $4A$
  • D
    $\sqrt{2}\text{A}$

Answer: A.

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Q 4M.C.Q (1 Marks)1 Mark
Which of the following statements are true for a stationary wave?
  • A
    Every particle has a fixed amplitude which is different from the amplitude of its nearest particle.
  • B
    All the particles cross their mean position at the same time.
  • C
    There is no net transfer of energy across any plane.
  • ✓
    All of the above

Answer: D.

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Q 5M.C.Q (1 Marks)1 Mark
Speed of sound waves in a fluid depends upon:
  • A
    Directty on density of the medium.
  • B
    Square of Bulk modulus of the medium.
  • C
    Inversly on the square root of density.
  • ✓
    Directly on the square root of bulk modulus of the medium.

Answer: D.

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Q 7Fill In The Blanks[1 Marks ]1 Mark
A point source emits sound equally in all directions in a non$-$absorbing medium. Two points $P$ and $Q$ are at distances of $2m$ and $3m$ respectively from the source. The ratio of the intensities of the waves at $P$ and $Q$ is:
  • A
    $3 : 2$
  • B
    $2 : 3$
  • ✓
    $9 : 4$
  • D
    $4 : 9$

Answer: C.

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Q 131 Marks Question1 Mark
For the travelling harmonic wave
$\text{y}(\text{x, t})=2.0\cos2\pi(10\text{t}-0.0080\text{x}+0.35)$
where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of
0.5m,
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Q 141 Marks Question1 Mark
For the travelling harmonic wave
$\text{y}(\text{x, t})=2.0\cos2\pi(10\text{t}-0.0080\text{x}+0.35)$
where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of
4m.
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Q 151 Marks Question1 Mark
Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a travelling wave, (ii) a stationary wave or (iii) none at all:
$\text{y}=\cos\text{x}\sin\text{t}+\cos2\text{x}\sin2\text{t}$
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Q 172 Marks Questions2 Marks
You have learnt that a travelling wave in one dimension is represented by a function $y=f(x, t)$ where $x$ and $t$ must appear in the combination $x-v t$ or $x+v t$, i.e. $y=f(x \pm v t)$. Is the converse true? Examine if the following functions for $y$ can possibly represent a travelling wave:
a. $(x-v t)^2$
b. $\log \left[(x+v t) / x_0\right]$
c. $1 /(x+v t)$
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Q 182 Marks Questions2 Marks
A transverse harmonic wave on a string is described by
$\text{y}(\text{x, t})=3.0\sin\big(36\text{t}+0.018\text{x}+\frac{\pi}{4}\big)$
where x and y are in cm and t in s. The positive direction of x is from left to right.
What are its amplitude and frequency?
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Q 213 Marks Question3 Marks
A steel wire has a length of $12.0m$ and a mass of $2.10kg$. What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at $20^\circ C = 343m s^{–1}$.
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Q 223 Marks Question3 Marks
A bat emits ultrasonic sound of frequency $1000 kHz$ in air. If the sound meets a water surface, what is the wavelength of (a) the reflected sound, (b) the transmitted sound? Speed of sound in air is $340m s^{–1}$ and in water $1486m s^{–1}$.
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Q 233 Marks Question3 Marks
A hospital uses an ultrasonic scanner to locate tumours in a tissue. What is the wavelength of sound in the tissue in which the speed of sound is $1.7km s^{–1}$? The operating frequency of the scanner is $4.2$ MHz.
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Q 243 Marks Question3 Marks
A SONAR system fixed in a submarine operates at a frequency $40.0 kHz$. An enemy submarine moves towards the $SONAR$ with a speed of $360km h^{–1}$. What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be $1450m s^{–1}.$
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Q 253 Marks Question3 Marks
A string of mass 2.50kg is under a tension of 200N. The length of the stretched string is 20.0m. If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?
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Q 265 Marks Questions5 Marks
The transverse displacement of a string (clamped at its both ends) is given by
$\text{y}(\text{x, t})=0.06\sin\Big(\frac{2\pi}{3}\text{x}\Big)\cos(120\pi\text{ t})$
where x and y are in m and t in s. The length of the string is 1.5m and its mass is $3.0 \times 10^{–2}kg$.
Answer the following:
Interpret the wave as a superposition of two waves travelling in opposite directions. What is the wavelength, frequency, and speed of each wave?
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Q 275 Marks Questions5 Marks
A pipe $20cm$ long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a $430Hz$ source? Will the same source be in resonance with the pipe if both ends are open? (speed of sound in air is $340m s^{–1}$).
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Q 285 Marks Questions5 Marks
A wire stretched between two rigid supports vibrates in its fundamental mode with a frequency of $45Hz$. The mass of the wire is $3.5 \times 10^{–2}kg$ and its linear mass density is $4.0 \times 10^{–2}kg m^{–1}$. What is
  1. The speed of a transverse wave on the string,
  2. The tension in the string?
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Q 295 Marks Questions5 Marks
For the wave described in Exercise 15.8, plot the displacement (y) versus (t) graphs for x = 0, 2 and 4cm. What are the shapes of these graphs? In which aspects does the oscillatory motion in travelling wave differ from one point to another: amplitude, frequency or phase?
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Q 305 Marks Questions5 Marks
One end of a long string of linear mass density $8.0 \times 10^{–3}kg m^{–1}$ is connected to an electrically driven tuning fork of frequency $256Hz$. The other end passes over a pulley and is tied to a pan containing a mass of $90kg$. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At $t = 0$, the left end (fork end) of the string $x = 0$ has zero transverse displacement $(y = 0)$ and is moving along positive y-direction. The amplitude of the wave is $5.0cm$. Write down the transverse displacement y as function of x and t that describes the wave on the string.
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Q 31Case study (4 Marks)4 Marks
Read the passage given below and answer the following questions from 1 to 5. Beat The phenomenon of regular variation in intensity of sound with time at a particular position due to superposition of two sound waves of slightly different frequencies is called beats. For waves
$\therefore\text{y}=2\text{a}\cos\pi(\text{v}_1-\text{v}_2)\text{t}.\sin\pi(\text{v}_1-\text{v}_2)\text{t}$ is the required equation of beats. Beat frequency is given by $\text{v}_{\text{beat}}=\text{v}_1-\text{v}_2$ Beat period is given by
$\text{T}=\frac{1}{\text{Beat frequency}}=\frac{1}{\text{v}_1-\text{v}_2}$
  1. Which of the following phenomenon is used by the musicians to tune their musical instruments?
  1. Interference
  2. Diffraction
  3. Beats
  4. Polarisation
  1. The phenomenon of beats can take place
  1. For longitudinal waves only
  2. For transverse wave only
  3. For sound waves only
  4. For both longitudinal and transverse waves
  1. When two waves of almost equal frequencies $v_1$ and $v_2$ reach at a point simultaneously, the time interval between successive maxima is:
  1. $\text{v}_1+\text{v}_2$
  2. $\text{v}_1-\text{v}_2$
  3. $\frac{1}{\text{v}_1+\text{v}_2}$
  4. $\frac{1}{\text{v}_1-\text{v}_2}$
  1. Two turning forks of frequencies $n_1$ and $n_2$ produces n beats per second. If $n_2$ and n are known, $n_1$ may be given by:
  1. $\frac{\text{n}_2}{\text{n}}+\text{n}_2$
  2. $\text{n}_2\text{n}$
  3. $\text{n}_2\pm\text{n}$
  4. $\frac{\text{n}_2}{\text{n}}-\text{n}_2$
  1. P and Q are two wires whose fundamental frequencies are 256 Hz and 382 Hz respectively. How many beats in two seconds will be heard by the third harmonic of A and second harmonic of B?
  1. 4
  2. 8
  3. 16
  4. zero
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Q 32Case study (4 Marks)4 Marks
Read the passage given below and answer the following questions from 1 to 5.
What happens if a pulse or a wave meets a boundary? If the boundary is rigid, pulse travelling along a stretched string and being reflected by the boundary. Assuming there is no absorption of energy by the boundary, the reflected wave has the same shape as the incident pulse i.e. crest is reflected as crest and trough as trough but it suffers a phase change of π or $180^0$ on reflection. This is because the boundary is rigid and the disturbance must have zero displacement at all times at the boundary. By the principle of superposition, this is possible only if the reflected and incident waves differ by a phase of π, so that the resultant displacement is zero. This reasoning is based on boundary condition on a rigid wall. If on the other hand, the boundary point is not rigid but completely free to move (such as in the case of a string tied to a freely moving ring on a rod), the reflected pulse has the same phase and amplitude (assuming no energy dissipation) as the incident pulse. The net maximum displacement at the boundary is then twice the amplitude of each pulse. An example of non- rigid boundary is the open end of an organ pipe. To summaries, a travelling wave or pulse suffers a phase change of π on reflection at a rigid boundary and no phase change on reflection at an open boundary. We considered above reflection at one boundary. But there are familiar situations (a string fixed at either end or an air column in a pipe with either end closed) in which reflection takes place at two or more boundaries. In a string, for example, a wave travelling in one direction will get reflected at one end, which in turn will travel and get reflected from the other end. This will go on until there is a steady wave pattern set up on the string. Such wave patterns are called standing waves or stationary waves.
  1. A travelling wave or pulse suffers a phase change of π on reflection at:
  1. A rigid boundary
  2. Open boundary
  1. A travelling wave or pulse suffers no phase change on reflection at:
  1. A rigid boundary
  2. Open boundary
  1. What are stationary waves?
  1. Write a note on reflection of travelling wave from rigid boundary.
  1. Write a note on reflection of travelling wave from open boundary.
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Q 33Case study (4 Marks)4 Marks
Read the passage given below and answer the following questions from 1 to 5.
Transverse and Longitudinal Waves Transverse waves forms if the particles of the medium vibrate at right angle to the direction of wave motion energy propagation, the wave is called transverse wave. These are propagated as crests and troughs.

Longitudinal waves forms if the particles of the medium vibrate in the direction of wave motion, the wave is called longitudinal. These are propagated as compressions and rarefactions and wave is also known as pressure or compressional wave. Wave on spring or sound waves in air are examples of longitudinal waves.
  1. In a transverse wave, the particles of the medium:
  1. Vibrate in a direction perpendicular to the direction of the propagation.
  2. Vibrate in a direction parallel to the direction of the propagation.
  3. Move in circle.
  4. Move in ellipse.
  1. A transverse wave consists of:
  1. Only crests
  2. Only troughs
  3. Both crests and troughs
  4. Rarefactions and compressions
  1. Ultrasonic waves produced by a vibrating quartz crystal are:
  1. Only longitudinal.
  2. Only transverse.
  3. Both longitudinal and transverse.
  4. Neither longitudinal nor transverse.
  1. Sound waves travel fastest in:
  1. Solids
  2. Liquids
  3. Gases
  4. Vacuum
  1. Sound waves in air cannot be polarized because:
  1. Their speed is small
  2. They require medium
  3. They are longitudinal
  4. Their speed is temperature dependent
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Q 34Case study (4 Marks)4 Marks
Read the passage given below and answer the following questions from 1 to 5.
When we speak, the sound moves outward from us, without any flow of air from one part of the medium to another. The disturbances produced in air are much less obvious and only our ears or a microphone can detect them. These patterns, which move without the actual physical transfer or flow of matter as a whole, are called waves. The most familiar type of waves such as waves on a string, water waves, sound waves, seismic waves, etc. is the so-called mechanical waves. These waves require a medium for propagation, they cannot propagate through vacuum. They involve oscillations of constituent particles and depend on the elastic properties of the medium. The electromagnetic waves that you will learn in Class XII are a different type of wave. Electromagnetic waves do not necessarily require a medium – they can travel through vacuum. Light, radio waves, X-rays, are all electromagnetic waves. We have seen that motion of mechanical waves involves oscillations of constituents of the medium. If the constituents of the medium oscillate perpendicular to the direction of wave propagation, we call the wave a transverse wave. If they oscillate along the direction of wave propagation, we call the wave a longitudinal wave. In transverse waves, the particle motion is normal to the direction of propagation of the wave. Therefore, as the wave propagates, each element of the medium undergoes a shearing strain. Transverse waves can, therefore, be propagated only in those media, which can sustain shearing stress, such as solids and not in fluids. Fluids, as well as, solids can sustain compressive strain; therefore, longitudinal waves can be propagated in all elastic media.
For example, in medium like steel, both transverse and longitudinal waves can propagate, while air can sustain only longitudinal waves. Answer the following.
  1. Air can sustain:
  1. Transverse waves
  2. Longitudinal waves
  3. Both a and b
  4. None of these
  1. The electromagnetic waves can pass through
  1. Solids only
  2. Fluids only
  3. Any medium even through vacuum
  4. None of these
  1. Define Transverse waves
  1. Define longitudinal waves
  1. Differentiate between Transverse waves and longitudinal waves
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Q 35Case study (4 Marks)4 Marks
Read the passage given below and answer the following questions from 1 to 5.
Beats is an interesting phenomenon arising from interference of waves. When two harmonic Sound waves of slightly different frequencies and comparable amplitude are heard at the same time, we hear a sound of similar frequency (the average of two close frequencies), but we hear something else also. We hear audibly distinct waxing and waning of the intensity of the sound, with a frequency equal to the difference in the two close frequencies. Beat frequency is given by
$u = u_1 - u_2$
Artists use this phenomenon often while tuning their instruments with each other. They go on tuning until their sensitive ears do not detect any beats.
Doppler Effect is a wave phenomenon, it holds not only for sound waves but also for electromagnetic waves. However, here we shall consider only sound waves. Doppler Effect is defined as increase or decrease in frequency of sound due to relative motion between source of sound and observer. Frequency increases when source and observer comes towards each other and frequency decreases when source and observer go away from each other .For sound the observed frequency n is given in terms of the source frequency $v_0$ by
$\text{u}=\text{v}_0\frac{\text{v}+\text{v}_0}{\text{v}+\text{vs}}$
Here v is the speed of sound through the medium, is the velocity of observer relative to the medium, and is the source velocity relative to the medium. In using this formula, velocities in the direction OS should be treated as positive and those opposite to it should be taken to be negative. The change in frequency caused by a moving object due to Doppler Effect is used to measure their velocities in diverse areas such as military, medical science, astrophysics, etc. It is also used by police to check over-speeding of vehicles. A sound wave or electromagnetic wave of known frequency is sent towards a moving object. Some part of the wave is reflected from the object and its frequency is detected by the monitoring station. This change in frequency is called Doppler shift. It is used at airports to guide aircraft, and in the military to detect enemy aircraft. Astrophysicists use it to measure the velocities of stars. Doctors use it to study heart beats and blood flow in different parts of the body. Here they use ultrasonic waves, and in common practice, it is called sonography. Ultrasonic waves enter the body of the person, some of them are reflected back, and give information about motion of blood and pulsation of heart valves, as well as pulsation of the heart of the foetus. In the case of heart, the picture generated is called echocardiogram. Answer the following
  1. Beats are heard after superposition of two waves with beat frequency.
  1. $υ = υ_1 - υ_2$
  2. $υ = υ_1 + υ_2$
  3. $υ = (υ_1 - υ_2)/_2$
  4. None of these
  1. When source and observer comes towards each other then frequency heard will.
  1. Increase
  2. Decrease
  3. Remains same
  4. None of these
  1. Define beats.
  1. Define Doppler effect in sound.
  1. Note on applications of Doppler Effect in sound.
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