Physics Multiple Choice Questions 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
Answer: b
Clarification: 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)
Answer: a
Clarification: 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?
a) True
b) False
Answer: a
Clarification: 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?
a) λ
b) λ/2
c) 2λ
d) λ/4
Answer: d
Clarification: 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.
a) 2λ
b) λ
c) 4λ
d) λ/4
Answer: a
Clarification: 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
= 2λ.
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?
a) λ/2
b) λ
c) 2λ
d) λ/4
Answer: d
Clarification: 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
= 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.
a) 34m
b) 68m
c) 17m
d) 51m
Answer: a
Clarification: 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
= 34m.
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
Answer: d
Clarification: 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?
a) 0.5Hz
b) 2Hz
c) 4Hz
d) 1Hz
Answer: b
Clarification: 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?
a) True
b) False
Answer: b
Clarification: 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.