This set of Physics Multiple Choice Questions & Answers (MCQs) focuses on “Reflection of Waves”.
1. If a string wave encounters a completely fixed end, what happens to its phase?
a) Stays the same
b) Changes by π
c) Changes by π/2
d) Waves gets destroyed
Explanation: The reason for the phase to change by π is that the boundary displacement should be zero because it is rigid & by principle of superposition it is only possible if the reflected wave differs by a phase of π.
2. The equation of a wave is: y = 2sin(4x-3t). What will be the equation of the reflected wave from a free surface?
a) y = 2sin(4x+3t)
b) y = 2sin(3t-4x)
c) y = 2cos(4x+3t)
d) y = 2sin(4x-3t)
Explanation: At the free surface reflected wave suffers no phase change.
Only the direction of wave propagation gets reversed.
So, the equation will be y = 2sin(4x+3t).
3. In a standing wave the amplitude of a particle is fixed, but varies from particle to particle. True or False?
Explanation: A standing wave neither moves left or right, all particles between two nodes are in the same phase. The equation of a standing wave is of the form Asin(kx)cos(wt),
where Asin(kx) is the amplitude which is different for different values of x.
This shows that for each value of x we get a different value of amplitude.
4. What is the minimum distance between a node & an antinode in a standing wave?
Explanation: The amplitude in a standing wave is given by Asin(kx).
Node is a point where amplitude is zero and antinode is a point where amplitude is maximum.
For a node, sin(kx) = 0
kx = 2nπ OR (2π/λ)x = nππ
x = nλ/2.
For an antinode, sin(kx) = 1
kx = (2n+1)π/2
(2π/λ)x = (2n+1)π/2
x = (2n+1) λ/4.
∴ node is at λ/2, λ, 3λ/2 …
& antinode at λ/4, 3λ/4, 5λ/4 …
∴ minimum distance = λ/2 – λ/4 = λ/4.
5. If a standing wave is vibrating in the fourth harmonic and the wavelength is λ, what is the length of the string.
Explanation: If the length of string is L, then the wavelength of the standing wave is 2L/n.
Or we can say L = nλ/2, where n corresponds to nth harmonic.
∴ L = 4λ/2
6. Consider the case of normal modes of vibration for the air column with only one end closed. What is the length of the air column for the fundamental harmonic?
Explanation: For the given condition wavelength is related to length by: λ = 4L/(2n+1).
∴ For fundamental harmonic n=0, & L = (2n+1)λ/4
= (0 + 1)λ/4
7. A pipe is open at both ends. What should be its length such that it resonates a 10Hz source in the 2nd harmonic? Speed of sound in air = 340m/s.
Explanation: For a pipe open at both ends frequency ‘f’ = nv/2L, where n is speed of sound.
Given: f = 10 & n=2.
∴ 10 = 2*340/2L
∴ L = 680/20
8. Consider standing waves in an air column with one end closed. What is a pressure node?
a) Pressure variation is maximum
b) Displacement variation is minimum
c) Same as displacement node
d) Least pressure change
Explanation: The point where there is an antinode corresponds to maximum amplitude of displacement. This also implies that here, pressure changes are minimum and it is therefore called a pressure node.
9. A pipe open at both ends has a fundamental frequency of 2Hz. If the pipe is closed at one end and half filled with water, what will be the fundamental frequency?
Explanation: The fundamental frequency in the first case is given by: f1 = v/2L.
In the second case length becomes half & one end is closed,
so fundamental frequency f2 = v/(4L/2)
= v/2L = f1.
So the value of f2 = 2Hz.
10. Standing waves can be produced when two identical waves, having a phase difference of π, are travelling in the same direction. True or False?
Explanation: The equation of standing waves is given by; y = Asin(kx)cos(wt).
This is formed by adding two waves of the form asin(kx-wt) & bsin(kx+wt)
which shows that they both must be travelling in opposite directions.
Sanfoundry Global Education & Learning Series – Physics – Class 11.
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