Q#1
A mechanical wave propagates in a medium along the X-axis. The particles of the medium(a) must move on the X-axis
(b) must move on the Y-axis
(c) may move on the X-axis
(b) may move on the Y-axis
Answer: (c), (d)
Mechanical waves are either transverse or longitudinal. In the transverse wave, the particles will move on Y-axis while in the longitudinal wave the particles will move on X-axis. So the particles of the medium may move on the X-axis or it may move on the Y-axis depending upon the nature of the wave.
Q#2
A transverse wave travels along the Z-axis. The particles of the medium must move
(a) along the Z-axis
(b) along the X-axis
(c) along the Y-axis
(d) in the X-Y plane.
Answer: (d)
The particles of the medium move perpendicular to the direction of the propagation of the wave in the case of a transverse wave. Here the wave travels along the Z-axis. All the lines in the X-Y plane are perpendicular to Z-axis, hence the particles of the medium must move in the X-Y plane.
Q#3
Longitudinal waves cannot
(a) have a unique wavelength
(b) transmit energy
(c) have a unique wave velocity
(d) be polarized.
Answer: (d)
All the three options (a), (b) and (c) are not true.
The particles of the medium in a longitudinal wave move along the direction of the wave. Hence it cannot be polarized with a slit.
Q#4
A wave going in a solid
(a) must be longitudinal
(b) maybe longitudinal
(c) must be transverse
(d) maybe transverse
Answer: (b), (d)
Both types of wave can travel through a solid. So it can either be a longitudinal wave or a transverse wave.
Q#5
A wave moving in a gas
(a) must be longitudinal
(b) maybe longitudinal
(c) must be transverse
(d) maybe transverse
Answer: (a)
Only a longitudinal wave can move in a gas because the particles of the gas are not close enough to allow a transverse wave.
Q#6
Two particles A and B have a phase difference of π when a sine wave passes through the regions.
(a) A oscillates at half the frequency of B
(b) A and B move in opposite directions.
(c) A and B must be separated by half of the wavelength.
(d) The displacements at A and B have equal magnitudes.
Answer: (b), (d)
The frequencies of the particles will be the same, so the option (a) is not true.
Let the displacement of the particle at A be
y = A' sin(⍵t – kx)
and of the particle at B be
y' = A' sin(⍵t – kx + π) = -A' sin(⍵t – kx)
So, y = -y'.
Thus A and B move in opposite directions and the displacements at A and B have equal magnitudes. So, the options (b) and (d) are true.
When the phase difference of A and B is π, the separation between them maybe (nλ + λ/2) = (2n + 1)λ/2, where n = 1, 2, 3,....... The option (c) is a special case, hence not true.
Q#7
A wave is represented by the equation
y = (0.001 mm) sin[(50 s⁻¹)t + (2.0 m⁻¹)x]
(a) The wave velocity = 100 m/s
(b) The wavelength = 2.0 m.
(c) The frequency = 25/π Hz.
(d) The amplitude = 0.001 mm.
Answer: (c), (d)
Comparing with a wave equation
y = A sin ⍵(t – x/v)
⍵ = 50 s⁻¹, ⍵/v = -2
v = -50/2 = -25 m/s. Hence the option (a) is not true.
2π/λ = ⍵/v = -2,
λ = -2π/2 = -π m
Hence the option (b) is not true.
⍵ = 50 s⁻¹
frequency = ⍵/2π = 50/(2π) = 25/π Hz
Hence option (c) is true.Amplitude = 0.001 mm. Option (d) is correct.
Q#8
A standing wave is produced on a string clamped at one end and free at the other. The length of the string
(a) must be an integral multiple of λ/4
(b) must be an integral multiple of λ/2
(c) must be an integral multiple of λ
(d) may be an integral multiple of λ/2.
Answer: (a)
For the given end conditions, standing waves are produced if
ν = (n + ½)v/2L
v/𝜆 = (n + ½)v/2L
L = (n + ½)𝜆/2 = (2n + 1)𝜆/4, where n = 0, 1, 2, ....
Thus the length of the string is an integral multiple of 𝜆/4.
Q#9
Mark out the correct options.
(a) The energy of any small part of a string remains constant in a traveling wave.
(b) The energy of any small part of a string remains constant in a standing wave.
(c) The energies of all the small parts of equal length are equal in a traveling wave.
(d) The energies of all the small parts of equal length are equal in a standing wave.
ν = (n + ½)v/2L
v/𝜆 = (n + ½)v/2L
L = (n + ½)𝜆/2 = (2n + 1)𝜆/4, where n = 0, 1, 2, ....
Thus the length of the string is an integral multiple of 𝜆/4.
Q#9
Mark out the correct options.
(a) The energy of any small part of a string remains constant in a traveling wave.
(b) The energy of any small part of a string remains constant in a standing wave.
(c) The energies of all the small parts of equal length are equal in a traveling wave.
(d) The energies of all the small parts of equal length are equal in a standing wave.
Answer: (b)
In a traveling wave, energy is transmitted from one region of space to other but in a standing wave, the energy of one region is always confined in that region. Hence option (b) is true.
Q#10
In a stationary wave.
(a) all the particles of the medium vibrate in phase
(b) all the antinodes vibrate in phase
(c) the alternate antinodes vibrate in phase
(d) all the particles between consecutive nodes vibrate in phase.
Answer: (c), (d)
In a stationary wave, all the particles between consecutive nodes vibrate in phase. Option (d) is correct.
The particles on the different sides of a node do not vibrate in phase but they have a phase difference of π. So the alternate parts between the consecutive nodes vibrate in phase. Thus the options (a) and (b) are not true but (c) is true.
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