1. A wave travelling along a rope is best described as
ⓐ. a permanent transfer of rope material from one end to the other
ⓑ. a force that exists only at the point where the rope is held
ⓒ. a particle that leaves the rope and moves forward
ⓓ. a disturbance that moves through the rope while carrying energy
Correct Answer: a disturbance that moves through the rope while carrying energy
Explanation: A wave is a travelling disturbance. In a rope wave, different parts of the rope move from their mean positions, but the rope as a whole does not travel along with the wave. The disturbance carries energy from one place to another. The material particles of the medium only take part in local motion around their equilibrium positions. This is why wave motion is different from throwing an object from one place to another. The central idea is energy transfer through a disturbance, not permanent transport of the medium.
2. A cork floating on water moves up and down as ripples pass across the surface. The ripples travel outward, but the cork does not travel outward with them. This observation mainly shows that
ⓐ. water ripples move only matter and transfer no energy
ⓑ. the cork and water surface remain completely at rest
ⓒ. waves can exist only when the water is very deep
ⓓ. disturbance moves while water is not transported
Correct Answer: disturbance moves while water is not transported
Explanation: The cork follows the local motion of the water surface near its position. It oscillates up and down as the disturbance passes, but it does not move along with the outward spread of the ripple. This shows the difference between wave propagation and bulk motion of matter. The wave carries energy across the surface, while the water particles mainly oscillate near their mean positions. A floating object may drift slightly due to other effects, but that is not the basic wave motion being described. The observation separates travelling disturbance from permanent transport of water.
3. In basic wave language, the quantity \(y\) in a displacement wave usually represents
ⓐ. displacement of a particle from its mean position
ⓑ. distance travelled by the whole medium during the wave
ⓒ. speed of the source as it produces the disturbance
ⓓ. total mass transported by the wave
Correct Answer: displacement of a particle from its mean position
Explanation: In a displacement wave, \(y\) commonly denotes the displacement of a particle of the medium from its equilibrium or mean position. It is not the distance travelled by the wave itself. The position along the direction of propagation is usually represented by \(x\), while time is represented by \(t\). The wave may move forward, but a medium particle is described by its displacement \(y\) at a given \(x\) and \(t\). This distinction becomes important later when reading equations such as \(y(x,t)\). Confusing \(y\) with the distance travelled by the wave hides the difference between particle motion and wave motion.
4. The pair that represents a wave quantity and its usual SI unit is
ⓐ. frequency \(f\) and \(\text{m}\)
ⓑ. wavelength \(\lambda\) and \(\text{s}\)
ⓒ. time period \(T\) and \(\text{s}\)
ⓓ. wave speed \(v\) and \(\text{Hz}\)
Correct Answer: time period \(T\) and \(\text{s}\)
Explanation: Time period \(T\) is the time taken for one complete oscillation, so its SI unit is \(\text{s}\). Frequency \(f\) is measured in \(\text{Hz}\), not in \(\text{m}\). Wavelength \(\lambda\) is a length, so it is measured in \(\text{m}\), not in \(\text{s}\). Wave speed \(v\) is measured in \(\text{m s}^{-1}\), not in \(\text{Hz}\). The symbols are useful only when their physical meanings and units are kept together. A unit mismatch usually means the wave quantity has been identified wrongly.
5. A disturbance moves through air from a vibrating tuning fork to a listener. During this process, the air particles
ⓐ. move permanently from the fork to the listener
ⓑ. oscillate about their mean positions while energy travels
ⓒ. remain completely at rest because only sound energy moves
ⓓ. travel faster than the disturbance in the direction of sound
Correct Answer: oscillate about their mean positions while energy travels
Explanation: Sound in air is produced by disturbances of pressure and density. The air particles do not move permanently from the source to the listener. They oscillate about their mean positions and pass the disturbance to neighbouring particles. The energy of the sound wave travels through the air because of these local oscillations. If air itself moved bodily from the source to the listener, sound would be a bulk flow rather than a wave. The particle motion is local, while the disturbance moves through the medium.
6. The amplitude \(A\) of a wave refers to
ⓐ. the distance between two neighbouring crests
ⓑ. the number of oscillations per second
ⓒ. the time taken for one complete oscillation
ⓓ. maximum displacement from the mean position
Correct Answer: maximum displacement from the mean position
Explanation: Amplitude \(A\) measures the largest displacement of a particle of the medium from its mean position. It tells how far the particle moves on either side of equilibrium during the oscillation. The distance between neighbouring crests is wavelength \(\lambda\), not amplitude. The number of oscillations per second is frequency \(f\), while the time for one oscillation is time period \(T\). Amplitude is therefore a measure of the size of the disturbance. It should not be confused with the distance over which the wave pattern repeats.
7. Use the graph description below.
A snapshot of a water wave is drawn as displacement \(y\) against position \(x\). Two nearest crests are marked on the curve.
The horizontal distance between these two nearest crests gives
ⓐ. wavelength
ⓑ. amplitude
ⓒ. time period
ⓓ. frequency
Correct Answer: wavelength
Explanation: In a displacement-position graph, the horizontal axis gives position \(x\). The distance between two nearest points in the same phase is the wavelength \(\lambda\). Two nearest crests are in the same phase because both represent maximum positive displacement in the same stage of oscillation. Amplitude \(A\) would be read vertically from the mean line to a crest. Time period \(T\) and frequency \(f\) are time-related quantities, so they are not directly measured as horizontal distances on a \(y-x\) snapshot. A spatial graph gives the pattern in space at one instant.
8. The statement “frequency is \(20\,\text{Hz}\)” means that
ⓐ. one oscillation takes \(20\,\text{s}\)
ⓑ. the wavelength is \(20\,\text{m}\)
ⓒ. \(20\) oscillations occur in \(1\,\text{s}\)
ⓓ. the wave speed is \(20\,\text{m s}^{-1}\)
Correct Answer: \(20\) oscillations occur in \(1\,\text{s}\)
Explanation: Frequency \(f\) is the number of complete oscillations per unit time. The unit \(\text{Hz}\) means \(\text{s}^{-1}\), so \(20\,\text{Hz}\) means \(20\) oscillations every \(1\,\text{s}\). It does not directly state the wavelength or wave speed. The time taken for one oscillation is the time period \(T\), and it is related by \(f=\frac{1}{T}\). Thus, a larger frequency means more oscillations in the same time interval. The unit \(\text{Hz}\) should be read as a rate of repetition, not as a length or speed.
9. Match the basic wave symbols with their meanings.
| Symbol | Meaning |
|---|
| P. \(A\) | 1. Time for one complete oscillation |
| Q. \(\lambda\) | 2. Maximum displacement from mean position |
| R. \(T\) | 3. Distance between nearest points in the same phase |
| S. \(f\) | 4. Number of oscillations per second |
ⓐ. P-1, Q-2, R-3, S-4
ⓑ. P-2, Q-3, R-1, S-4
ⓒ. P-2, Q-1, R-3, S-4
ⓓ. P-3, Q-2, R-4, S-1
Correct Answer: P-2, Q-3, R-1, S-4
Explanation: Amplitude \(A\) is the maximum displacement from the mean position, so P matches \(2\). Wavelength \(\lambda\) is the distance between nearest points in the same phase, so Q matches \(3\). Time period \(T\) is the time for one complete oscillation, so R matches \(1\). Frequency \(f\) is the number of oscillations per second, so S matches \(4\). These four quantities form the first language needed for describing wave motion. The main separation is that \(A\) and \(\lambda\) describe size in displacement or space, while \(T\) and \(f\) describe repetition in time.
10. A particle of a medium completes one oscillation in \(0.020\,\text{s}\). What is the frequency of the wave motion at that point?
ⓐ. \(50\,\text{Hz}\)
ⓑ. \(20\,\text{Hz}\)
ⓒ. \(0.050\,\text{Hz}\)
ⓓ. \(0.020\,\text{Hz}\)
Correct Answer: \(50\,\text{Hz}\)
Explanation: \( \textbf{Given data:} \) Time period \(T=0.020\,\text{s}\).
\( \textbf{Required quantity:} \) Frequency \(f\).
\( \textbf{Relation used:} \)
\[
f=\frac{1}{T}
\]
This relation applies because frequency is the number of complete oscillations per second.
\( \textbf{Substitution:} \)
\[
f=\frac{1}{0.020\,\text{s}}
\]
\( \textbf{Writing the decimal clearly:} \)
\[
0.020=\frac{20}{1000}=\frac{1}{50}
\]
\( \textbf{Calculation:} \)
\[
f=50\,\text{s}^{-1}
\]
\( \textbf{Unit conversion:} \)
\[
1\,\text{s}^{-1}=1\,\text{Hz}
\]
\( \textbf{Final answer:} \) The frequency is \(50\,\text{Hz}\).
Taking \(0.020\,\text{s}\) itself as the frequency would interchange \(T\) and \(f\), which are reciprocal quantities.
11. The unit \(\text{m s}^{-1}\) is naturally associated with
ⓐ. amplitude \(A\)
ⓑ. wavelength \(\lambda\)
ⓒ. wave speed \(v\)
ⓓ. frequency \(f\)
Correct Answer: wave speed \(v\)
Explanation: Wave speed \(v\) tells how fast the disturbance travels through space, so it is measured as distance per unit time. The SI unit of distance is \(\text{m}\), and the SI unit of time is \(\text{s}\), giving \(\text{m s}^{-1}\). Amplitude \(A\) and wavelength \(\lambda\) are both lengths, so their unit is \(\text{m}\). Frequency \(f\) is measured in \(\text{Hz}\) or \(\text{s}^{-1}\). The unit itself helps identify the physical role of the quantity. A speed unit should point to propagation, not to the size or repetition rate of oscillation.
12. In the relation \(v=f\lambda\), the symbol \(v\) represents
ⓐ. maximum speed of one oscillating particle about its mean position
ⓑ. vertical displacement of a particle from equilibrium
ⓒ. number of oscillations made by the source in one second
ⓓ. propagation speed of the wave disturbance
Correct Answer: propagation speed of the wave disturbance
Explanation: The relation \(v=f\lambda\) connects the speed of the travelling wave with its frequency and wavelength. Here \(v\) is the propagation speed of the disturbance, not the speed of an individual medium particle during oscillation. A medium particle may move up and down or back and forth, depending on the wave type. The disturbance, however, moves from one region of the medium to another. Frequency \(f\) gives how often oscillations repeat, and wavelength \(\lambda\) gives the spatial repeat distance. The symbol \(v\) in this relation belongs to the travelling pattern, not to the local oscillatory motion of a particle.
13. Assertion: A wave can carry energy from one place to another without permanent transport of matter.
Reason: In a mechanical wave, particles of the medium generally oscillate about their mean positions.
ⓐ. Both Assertion and Reason are true, and Reason explains Assertion
ⓑ. Both Assertion and Reason are true, but Reason does not explain Assertion
ⓒ. Assertion is true, but Reason is false
ⓓ. Assertion is false, but Reason is true
Correct Answer: Both Assertion and Reason are true, and Reason explains Assertion
Explanation: The Assertion is true because wave motion is a way of transferring energy through a disturbance. In a mechanical wave, the material particles of the medium do not need to move permanently from the source to the receiver. They usually oscillate around mean positions and pass the disturbance to neighbouring particles. That local oscillation is the reason the disturbance can travel while the medium itself is not transported bodily. The Reason therefore gives the physical explanation of the Assertion. The idea is especially clear in rope waves, water ripples, and sound waves in air.
14. A stone thrown across a field and a ripple moving across water both involve motion. The motion of the stone is not a wave mainly because
ⓐ. the stone has no energy while moving
ⓑ. the stone material itself is transported
ⓒ. water can never show particle motion
ⓓ. a wave must always be visible to the eye
Correct Answer: the stone material itself is transported
Explanation: A thrown stone is an object moving bodily from one place to another. Its material itself is transported through space. A water ripple, in contrast, is a travelling disturbance of the water surface. The water particles mainly move locally while the wave pattern moves outward. Wave motion is identified by propagation of a disturbance, not by any motion whatsoever. The example of a thrown stone helps separate object motion from wave motion. Energy travels in both cases, but the mechanism of transport is different.
15. Study the table and choose the row with a mismatched unit.
| Row | Quantity | Unit |
|---|
| P | Amplitude \(A\) | \(\text{m}\) |
| Q | Time period \(T\) | \(\text{s}\) |
| R | Frequency \(f\) | \(\text{Hz}\) |
| S | Wavelength \(\lambda\) | \(\text{s}^{-1}\) |
ⓐ. Row P
ⓑ. Row Q
ⓒ. Row S
ⓓ. Row R
Correct Answer: Row S
Explanation: Wavelength \(\lambda\) is a distance, so its SI unit is \(\text{m}\). The unit \(\text{s}^{-1}\) belongs to frequency \(f\), and it is also written as \(\text{Hz}\). Row P is matched properly because amplitude \(A\) is also a displacement and is measured in \(\text{m}\). Row Q is proper because time period \(T\) is measured in \(\text{s}\). Row R is proper because frequency \(f\) is measured in \(\text{Hz}\). The mismatched row confuses a spatial repeat distance with a time-rate quantity.
16. A wave has frequency \(25\,\text{Hz}\) and wavelength \(0.40\,\text{m}\). What is its wave speed?
ⓐ. \(10\,\text{m s}^{-1}\)
ⓑ. \(62.5\,\text{m s}^{-1}\)
ⓒ. \(25.4\,\text{m s}^{-1}\)
ⓓ. \(0.016\,\text{m s}^{-1}\)
Correct Answer: \(10\,\text{m s}^{-1}\)
Explanation: \( \textbf{Given data:} \) Frequency \(f=25\,\text{Hz}=25\,\text{s}^{-1}\), wavelength \(\lambda=0.40\,\text{m}\).
\( \textbf{Required quantity:} \) Wave speed \(v\).
\( \textbf{Useful relation:} \)
\[
v=f\lambda
\]
This relation applies because the wave travels one wavelength in one time period, and \(f=\frac{1}{T}\).
\( \textbf{Substitution:} \)
\[
v=(25\,\text{s}^{-1})(0.40\,\text{m})
\]
\( \textbf{Calculation:} \)
\[
25\times0.40=10
\]
\( \textbf{Unit check:} \)
\[
\text{s}^{-1}\times\text{m}=\text{m s}^{-1}
\]
\( \textbf{Final answer:} \) The wave speed is \(10\,\text{m s}^{-1}\).
Dividing \(f\) by \(\lambda\) would give a unit \(\text{s}^{-1}\text{m}^{-1}\), which is not a speed.
17. Two statements about a simple travelling wave are given.
I. The medium particles may oscillate even when the wave pattern travels forward.
II. The wave speed always means the same thing as the instantaneous speed of a medium particle.
III. The wavelength is a spatial separation between nearest points in the same phase.
The supported statements are
ⓐ. I and II only
ⓑ. II and III only
ⓒ. I only
ⓓ. I and III only
Correct Answer: I and III only
Explanation: Statement I is supported because particles of a medium can oscillate locally while the wave disturbance travels forward. This is a basic feature of mechanical wave motion. Statement II is not supported because wave speed describes propagation of the disturbance, while particle speed describes local motion of a particle of the medium. These two speeds are physically different quantities. Statement III is supported because wavelength \(\lambda\) is the distance between nearest points that are in the same phase, such as neighbouring crests. The combination keeps particle motion, wave motion, and spatial repetition separate.
18. A sinusoidal wave is observed at one fixed point. The particle at that point returns to the same displacement and same direction of motion every \(0.10\,\text{s}\). The quantity \(0.10\,\text{s}\) is the
ⓐ. wavelength \(\lambda\)
ⓑ. time period \(T\)
ⓒ. wave speed \(v\)
ⓓ. amplitude \(A\)
Correct Answer: time period \(T\)
Explanation: At one fixed point, the motion being observed is the oscillation of a single medium particle. The time taken for that particle to return to the same state of motion is the time period \(T\). The phrase “same displacement and same direction of motion” indicates one complete oscillation. Wavelength \(\lambda\) is measured in space, not in time. Wave speed \(v\) tells how fast the disturbance travels, while amplitude \(A\) tells the maximum displacement. A time reading from one fixed point is naturally connected with \(T\), not with the spatial separation \(\lambda\).
19. A wave travels along a long spring. One coil of the spring is observed carefully as the disturbance passes. The coil should be expected to
ⓐ. move from the source end to the far end with the disturbance
ⓑ. remain fixed at its mean position at every instant
ⓒ. oscillate near its mean position as the disturbance passes
ⓓ. become the source of a new material stream through the spring
Correct Answer: oscillate near its mean position as the disturbance passes
Explanation: In a mechanical wave, the particles of the medium take part in local oscillatory motion. For a spring wave, each coil moves about its mean position as the disturbance passes through it. The disturbance can travel from one end to the other without the same coil being transported along the entire spring. The coil is not permanently carried with the wave pattern. It is also not motionless, because the wave requires local disturbance of the medium. This separates motion of medium particles from propagation of the wave disturbance.
20. The quantity that tells how many complete oscillations occur in \(1\,\text{s}\) is
ⓐ. wavelength \(\lambda\)
ⓑ. amplitude \(A\)
ⓒ. frequency \(f\)
ⓓ. wave speed \(v\)
Correct Answer: frequency \(f\)
Explanation: Frequency \(f\) counts the number of complete oscillations per second. Its SI unit is \(\text{Hz}\), which is the same as \(\text{s}^{-1}\). Wavelength \(\lambda\) measures spatial repetition, not time repetition. Amplitude \(A\) measures the maximum displacement from the mean position. Wave speed \(v\) tells how fast the disturbance travels through the medium. The phrase “per second” is the clue that the quantity is a rate of oscillation, not a length or displacement.
