A water wave moving horizontally across the surface of a pond causes a floating cork to mo… — JAMB UTME

A water wave moving horizontally across the surface of a pond causes a floating cork to move vertically up and down. The cork completes one full oscillation every $0.50\text{ s}$ , and the horizontal distance between two consecutive wave crests is $1.2\text{ m}$ . What is the speed of propagation of the wave, and how is the wave classified?

$2.4\text{ m s}^{-1}$ , transverse mechanical waveAnswer
B
$2.4\text{ m s}^{-1}$ , longitudinal mechanical wave
C
$0.60\text{ m s}^{-1}$ , transverse mechanical wave
D
$2.4\text{ m s}^{-1}$ , transverse electromagnetic wave

Answer

2.4\text{ m s}^{-1}

, transverse mechanical wave

The frequency of oscillation is

f = \frac{1}{T} = \frac{1}{0.50\text{ s}} = 2.0\text{ Hz}

. Using the wave formula

v = f\lambda

, the propagation speed is

v = 2.0\text{ Hz} \times 1.2\text{ m} = 2.4\text{ m s}^{-1}

. Because the cork vibrates vertically while the wave propagates horizontally, the oscillations are perpendicular to the propagation direction, defining a transverse wave. Since water is required for propagation, it is a mechanical wave.

Step-by-Step Solution

Determine the frequency of the wave from the period.

The period

T = 0.50\text{ s}

, so frequency

f = \frac{1}{T} = \frac{1}{0.50} = 2.0\text{ Hz}

Frequency is the reciprocal of the time period of oscillation.

Calculate the wave speed using the wave equation.

v = f \lambda = 2.0\text{ Hz} \times 1.2\text{ m} = 2.4\text{ m s}^{-1}

Wave speed equals the product of frequency and wavelength.

Classify the wave based on particle motion and medium requirement.

Particle displacement is perpendicular to wave direction (transverse) and requires water as a medium (mechanical).

Perpendicular oscillation defines transverse waves, and medium dependence defines mechanical waves.

Key Concept

Wave speed calculation and wave classification based on vibration direction and medium requirements.

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