Questions: Transverse Wave Characteristics and Properties

Question 1

A transverse wave travels along a horizontal string from left to right at 10 m/s. What is the motion of a single marked point on the string as the wave passes through it?

• A. It moves up and down perpendicular to the string, oscillating around its rest position
• B. It travels to the right at 10 m/s, carried along with the wave
• C. It moves diagonally, combining rightward travel with vertical oscillation
• D. It remains stationary except at the moment it sits exactly at the crest or trough

Answer: (A)

In a transverse wave, particles oscillate perpendicular to the direction of wave propagation — they move up and down but do not travel with the wave. The wave pattern and its energy propagate to the right; each individual particle stays in its local region and oscillates. This is the defining feature of transverse waves, and the central misconception to avoid: the wave transports energy, not matter.

Question 2

A wave has frequency 5 Hz and travels at 20 m/s through a medium. A second wave with frequency 10 Hz travels through the same medium at the same speed. What is the wavelength of the second wave?

• A. 2 m — since v = fλ and speed is constant, doubling frequency halves the wavelength
• B. 8 m — higher frequency produces a longer wavelength because the source is more energetic
• C. 4 m — same as the first wave, since both travel at the same speed through the same medium
• D. 40 m — speed times frequency gives wavelength

Answer: (A)

Using v = fλ: the first wave has λ₁ = v/f₁ = 20/5 = 4 m. For the second: λ₂ = v/f₂ = 20/10 = 2 m. With wave speed fixed by the medium, increasing frequency decreases wavelength proportionally. The misconception in option C is treating wavelength as determined solely by the medium; in fact, speed is determined by the medium while wavelength adjusts to satisfy v = fλ as the source frequency changes.

Question 3

In a transverse wave, individual particles move in the same direction as the wave travels.

• T. True
• F. False

Answer: False

This is the most common misconception about transverse waves. Particles oscillate perpendicular (transverse) to the direction of propagation. In a wave on a string traveling horizontally, particles move vertically. The wave — the traveling pattern of disturbance — moves horizontally, but individual particles do not. Energy is transported in the direction of travel; matter stays put and oscillates locally.

Question 4

The speed of a wave in a given medium is determined by the properties of that medium, not by the frequency or amplitude of the source.

• T. True
• F. False

Answer: True

Wave speed in a medium is a property of the medium itself — for a string, v = √(T/μ) where T is tension and μ is linear density. The source sets frequency; the medium sets speed; and wavelength adjusts to satisfy v = fλ. Changing source frequency changes wavelength but not speed. Amplitude also does not affect wave speed in linear media. This is why v = fλ is a constraint: given a fixed medium speed and a chosen source frequency, the wavelength is fully determined.

Question 5

Explain why a point on a string is moving fastest as a wave passes through its equilibrium position, but has zero speed when it is at a crest or trough.

Model answer: Each particle undergoes simple harmonic motion. At the crest or trough, the particle is at maximum displacement and instantaneously reversing direction — like a pendulum at its highest point — so its velocity is momentarily zero. At the equilibrium position, the restoring force has been accelerating the particle through its full range of motion, so it has maximum speed. This is the same energy trade-off as in SHM: maximum potential energy and zero kinetic energy at the extremes; maximum kinetic energy and zero potential energy at equilibrium.

Mathematically, if displacement is x(t) = A sin(ωt), velocity is v(t) = Aω cos(ωt). These are 90° out of phase: maximum displacement occurs at sin(ωt) = ±1, when cos(ωt) = 0 (zero velocity); maximum speed occurs at cos(ωt) = ±1, when sin(ωt) = 0 (equilibrium position). The particle passes through equilibrium with all kinetic energy and reaches the crest or trough with all potential energy.