A vibrating tuning fork generates a longitudinal sound wave in air. The fork completes 120… — JAMB UTME

A vibrating tuning fork generates a longitudinal sound wave in air. The fork completes $120$ full oscillations in $0.40\text{ s}$ . If the wavelength of the sound wave in air is $1.15\text{ m}$ , what is the speed of propagation of the wave in $\text{m/s}$ ?

Answer: 345 m/s

Answer

The speed of propagation of the sound wave in air is

345\text{ m/s}

The frequency of oscillation is determined by dividing the number of oscillations by the total time taken:

f = \frac{120}{0.40\text{ s}} = 300\text{ Hz}

. Substituting the frequency and given wavelength into the wave equation

v = f \lambda

yields

v = 300\text{ Hz} \times 1.15\text{ m} = 345\text{ m/s}

Step-by-Step Solution

Determine the frequency of the longitudinal wave.

f = 300\text{ Hz}

Frequency is the number of complete oscillations per unit time:

f = \frac{N}{t} = \frac{120}{0.40\text{ s}} = 300\text{ Hz}

Calculate the wave propagation speed using the wave equation.

v = 345\text{ m/s}

The speed of a progressive wave is given by

v = f \lambda = 300\text{ Hz} \times 1.15\text{ m} = 345\text{ m/s}

Key Concept

Relationship between frequency, wavelength, and wave propagation speed in a mechanical medium

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