MCQ/X11,15/Waves @jp

PHYSICS 22. A wave has a wavelength of 2 m and a frequency of

10 Hz. What is its speed?
Waves
23. A sound wave in air has a velocity of 340 m/s and a
X11,15 wavelength of 0.85 m. Calculate its frequency and
angular frequency.
1. Define wave motion and differentiate between me- 24. The displacement of a particle in a wave is given by
chanical waves and electromagnetic waves. y = 0.1 sin(2πt − πx). Calculate the time period of
the wave.
2. What is the principle of superposition of waves? Ex-
plain with an example. 25. A wave is traveling along a rope with a wave speed
of 20 m/s. If the frequency of the wave is 5 Hz, cal-
3. Derive the relation between the speed of a wave, its culate the distance between two consecutive crests.
frequency, and wavelength.
26. A wave equation is given as y = 0.02 sin(3πt − πx).
4. Explain the difference between transverse and lon- Find the wave velocity and the time taken for the
gitudinal waves with suitable examples. wave to travel a distance of 10 m.
5. What are standing waves? How are they formed? 27. The speed of a transverse wave on a stretched string
6. Define the terms amplitude, frequency, wavelength, is 60 m/s, and its frequency is 15 Hz. Calculate the
and wave velocity. wave number.
28. What are standing waves? Explain how they are

ES
7. What is wave interference? Distinguish between
constructive and destructive interference.
8. A wave is represented by the equation y(x, t) =
0.05 sin(4πx − 200πt). Calculate the wavelength,
frequency, and speed of the wave.
9. A wave travels with a velocity of 300 m/s and has a
frequency of 500 Hz. Calculate its wavelength.
10. The equation of a progressive wave is y =
0.03 sin(5t − 0.4x). Find the amplitude, angular fre-
quency, and wave number.
11. A sinusoidal wave travels along a string. Its dis-
placement is given by y = 0.02 cos(6πx + 120πt).
Determine the phase difference between two points
separated by 0.5 m.
12. A wave has a wavelength of 2 m and a frequency of
10 Hz. What is its speed?
formed.
29. Derive the equation for the formation of standing
waves in a stretched string.
30. Explain the conditions required for standing waves
to form in a medium.
31. What is the difference between nodes and antinodes
in standing waves?
32. A string of length 1 m is fixed at both ends. If the
speed of the wave on the string is 200 m/s, calculate
the frequency of the first three harmonics.
33. Explain the formation of standing waves in an air
column. Differentiate between open and closed
pipes.
34. A tube closed at one end resonates with a sound
wave of wavelength 1.2 m. Calculate the length of
the tube required to produce the fundamental fre-
DF
13. A sound wave in air has a velocity of 340 m/s and a
wavelength of 0.85 m. Calculate its frequency and quency.
angular frequency.
35. What is the relationship between the wavelength of
14. The displacement of a particle in a wave is given by a standing wave and the length of the string or pipe?
y = 0.1 sin(2πt − πx). Calculate the time period of
the wave. 36. Explain how the harmonics in standing waves differ
for open and closed pipes.
15. A wave is traveling along a rope with a wave speed
of 20 m/s. If the frequency of the wave is 5 Hz, cal- 37. In a stretched string, standing waves are formed
culate the distance between two consecutive crests. with a wavelength of 0.5 m. If the string is 2 m long,
how many loops will be formed?
16. A wave equation is given as y = 0.02 sin(3πt − πx).
Find the wave velocity and the time taken for the 38. Define wave motion. Differentiate between mechan-
wave to travel a distance of 10 m. ical waves and electromagnetic waves, providing ex-
amples of each.
17. The speed of a transverse wave on a stretched string
is 60 m/s, and its frequency is 15 Hz. Calculate the 39. Explain the concept of phase and phase difference
wave number. in wave motion. How do they affect the interference
of waves?
18. A wave is represented by the equation y(x, t) =
0.05 sin(4πx − 200πt). Calculate the wavelength, 40. Derive the relation between the speed of a wave, its
frequency, and speed of the wave. frequency, and wavelength. Explain its significance
in understanding wave propagation.
19. A wave travels with a velocity of 300 m/s and has a
frequency of 500 Hz. Calculate its wavelength.
20. The equation of a progressive wave is y =
0.03 sin(5t − 0.4x). Find the amplitude, angular fre-
quency, and wave number.
21. A sinusoidal wave travels along a string. Its dis-
placement is given by y = 0.02 cos(6πx + 120πt).
Determine the phase difference between two points
separated by 0.5 m.
MCQ/X11,15/Waves @jp

Solutions to Wave Motion Ques- 17. The speed of a transverse wave on

tions a stretched string is 60 m/s, and its fre-
quency is 15 Hz. Calculate the wave num-
1. Define wave motion and differentiate ber.
between mechanical waves and electro- Solution: Wavelength: λ = fv = 15 60
= 4 m. Wave
magnetic waves. number: k = 2π
= 2π
= 0.5π rad/m.
λ 4
Solution: Wave motion is the transfer of energy
through a medium or space without the transfer of mat- 28. What are standing waves? Explain
ter. Mechanical Waves: Require a medium (e.g.,
sound waves). Electromagnetic Waves: Do not re-
how they are formed.
quire a medium (e.g., light waves). Solution: Standing waves are formed when two waves
of the same frequency and amplitude traveling in oppo-
site directions superimpose. This creates nodes (points
8. A wave is represented by the equation of zero displacement) and antinodes (points of maximum
displacement).
y(x, t) = 0.05 sin(4πx − 200πt). Calculate the
wavelength, frequency, and speed of the
wave. Solutions to Other Questions
Solution: General form: y(x, t) = A sin(kx−ωt). Here, 2. What is the principle of superposition

ES
k = 4π, ω = 200π. Wavelength: λ = 2π
ω 200π

300 m/s and has a frequency of 500 Hz. add

Calculate its wavelength.
Solution: Wavelength: λ = v
f = 300
500

10. The equation of a progressive wave is

2π
k = 4π = 0.5 m. of waves? Explain with an example.
Frequency: f = 2π = 2π = 100 Hz. Speed: v = f λ =
100 · 0.5 = 50 m/s.

= 0.6 m.

y = 0.03 sin(5t − 0.4x). Find the amplitude,

angular frequency, and wave number.
Solution: General form: y = A sin(ωt − kx). Ampli-
Solution: The principle of superposition states that
when two or more waves pass through the same point in
space, the resultant displacement is the vector sum of the
displacements of the individual waves. Example: In in-
9. A wave travels with a velocity of terference, constructive interference occurs when waves
up, and destructive interference occurs when waves
cancel each other.

4. Explain the difference between trans-

verse and longitudinal waves with suitable
examples.
Solution: - Transverse Waves: The particles of the
medium vibrate perpendicular to the direction of wave
propagation. Example: Light waves, water waves. -
Longitudinal Waves: The particles of the medium vi-
brate parallel to the direction of wave propagation. Ex-
ample: Sound waves.
DF
tude: A = 0.03 m. Angular frequency: ω = 5 rad/s.
Wave number: k = 0.4 rad/m. 5. What are standing waves? How are
they formed?
12. A wave has a wavelength of 2 m and Solution: Standing waves are formed when two waves
a frequency of 10 Hz. What is its speed? of the same frequency and amplitude traveling in oppo-
site directions interfere. They create fixed points called
Solution: Speed: v = f λ = 10 · 2 = 20 m/s. nodes and points of maximum displacement called antin-
odes.

13. A sound wave in air has a veloc- 6. Define the terms amplitude, frequency,
ity of 340 m/s and a wavelength of 0.85 m. wavelength, and wave velocity.
Calculate its frequency and angular fre- Solution: - Amplitude: The maximum displacement
quency. of a wave from its equilibrium position. - Frequency:
The number of oscillations per unit time. - Wave-
Solution: Frequency: f = λv = 0.85
340
= 400 Hz. Angular length: The distance between two successive crests or
troughs in a wave. - Wave Velocity: The speed at
frequency: ω = 2πf = 2π · 400 = 800π rad/s. which the wave propagates through the medium.

16. A wave equation is given as y = 7. What is wave interference? Distin-

guish between constructive and destruc-
0.02 sin(3πt − πx). Find the wave velocity tive interference.
and the time taken for the wave to travel
a distance of 10 m. Solution: Wave interference occurs when two or more
waves overlap in the same region of space. - Construc-
Solution: General form: y = A sin(ωt − kx). Wave tive Interference: Occurs when the crest of one wave
number: k = π rad/m, Angular frequency: ω = aligns with the crest of another, resulting in an increased
amplitude. - Destructive Interference: Occurs when
3π rad/s. Wave velocity: v = ωk = 3π
π = 3 m/s. Time the crest of one wave aligns with the trough of another,
taken: t = distance
v = 10
3 = 3.33 s. resulting in decreased amplitude.
MCQ/X11,15/Waves @jp

14. The displacement of a particle in a 18. A wave is represented by the equation

wave is given by y = 0.1 sin(2πt − πx). Cal- y(x, t) = 0.05 sin(4πx − 200πt). Calculate the
culate the time period of the wave. wavelength, frequency, and speed of the
wave.
Solution: General form: y = A sin(ωt − kx). Angular
frequency: ω = 2π rad/s. Time period: T = 2π 2π Solution: Already solved as part of earlier solutions:
ω = 2π =
1 s. Wavelength: λ = 0.5 m. Frequency: f = 100 Hz. Speed:
v = 50 m/s.

15. A wave is traveling along a rope with 19. A wave travels with a velocity of
a wave speed of 20 m/s. If the frequency 300 m/s and has a frequency of 500 Hz.
of the wave is 5 Hz, calculate the distance Calculate its wavelength.
between two consecutive crests.
v 20 Solution: Already solved as part of earlier solutions:
Solution: Wavelength: λ = f = 5 = 4 m. Wavelength: λ = 0.6 m.

20. The equation of a progressive wave 22. A wave has a wavelength of 2 m and
is y = 0.03 sin(5t − 0.4x). Find the wave a frequency of 10 Hz. What is its speed?

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velocity and angular frequency.

to produce the fundamental frequency.

0.3 m.
Solution: Already solved as part of earlier solutions:
Solution: General form: y = A sin(ωt − kx). Wave
number: k = 0.4 rad/m. Angular frequency: ω =
5 rad/s. Wave velocity: v = ωk = 0.4 = 12.5 m/s.

with a sound wave of wavelength 1.2 m.

Speed: v = 20 m/s.

23. A sound wave in air has a veloc-

ity of 340 m/s and a wavelength of 0.85 m.
Calculate its frequency and angular fre-
34. A tube closed at one end resonates quency.
Calculate the length of the tube required Solution: Already solved as part of earlier solutions:
Frequency: f = 400 Hz. Angular frequency: ω =
800π rad/s.
Solution: For a tube closed at one end, L = λ
4 = 1.2
4 =
24. The displacement of a particle in a
wave is given by y = 0.1 sin(2πt − πx). Cal-
37. In a stretched string, standing waves culate the time period of the wave.
are formed with a wavelength of 0.5 m. If Solution: Already solved as part of earlier solutions:
DF
the string is 2 m long, how many loops will Time period: T = 1 s.
be formed?
2L 2·2
Solution: Number of loops: n = = = 8.
25. A wave is traveling along a rope with
λ 0.5
a wave speed of 20 m/s. If the frequency
of the wave is 5 Hz, calculate the distance
Answers to the Remaining Ques- between two consecutive crests.
tions Solution: Already solved as part of earlier solutions:
Wavelength: λ = 4 m.
3. Derive the relation between the speed
of a wave, its frequency, and wavelength.
Solution: The wave speed v is related to the fre-
26. A wave equation is given as y =
quency f and wavelength λ by the equation: v = f 0.02 sin(3πt − πx). Find the wave velocity
λT hisisderivedf romthedef initionof wavemotion, whereλand the time taken for the wave to travel
is the distance covered by one wave in one period, T = f1 . a distance of 10 m.
Thus, v = Tλ = f λ. Solution: Already solved as part of earlier solutions:
Wave velocity: v = 3 m/s. Time taken: t = 3.33 s.

11. A sinusoidal wave travels along a

string. Its displacement is given by y = 30. Explain the conditions required for
0.02 cos(6πx + 120πt). Determine the phase standing waves to form in a medium.
difference between two points separated Solution: Standing waves form when two waves of the
by 0.5 m. same frequency and amplitude traveling in opposite di-
rections interfere. Conditions: 1. The medium must
Solution: General form: y = A cos(kx + ωt). Wave have fixed boundaries. 2. The waves should have the
number: k = 6π rad/m. Phase difference: ∆ϕ = k∆x = same frequency and amplitude. 3. The interference must
6π · 0.5 = 3π rad. produce nodes and antinodes.
MCQ/X11,15/Waves @jp

31. What is the difference between nodes

and antinodes in standing waves?
Solution: - Nodes: Points of zero displacement where
destructive interference occurs. - Antinodes: Points of
maximum displacement where constructive interference
occurs.

35. What is the relationship between the

wavelength of a standing wave and the
length of the string or pipe?
Solution: For a string fixed at both ends: L =
nλ (2n−1)λ
2 (n=1,2,3,...)F orapipeopenatoneend:L= 4 (n=1,2,3,...)

36. Explain how the harmonics in stand-

ing waves differ for open and closed pipes.
Solution: - Open Pipe: Supports both even and odd
v
harmonics. Fundamental frequency: f = 2L . - Closed
Pipe: Supports only odd harmonics. Fundamental fre-

ES v
quency: f = 4L .
DF