The frequency of a wave is measured as (200 \pm 4)\text{ Hz} and its wavelength is measure… — JAMB UTME

The frequency of a wave is measured as $(200 \pm 4)\text{ Hz}$ and its wavelength is measured as $(0.50 \pm 0.01)\text{ m}$ . What is the maximum percentage error in the calculated speed of the wave?

A
$2.0\%$
$4.0\%$ Answer
C
$4.01\%$
D
$0.0\%$

Answer

The maximum percentage error in the calculated speed of the wave is

4.0\%

For a calculated quantity given by the product of two variables

v = f\lambda

, the fractional error is

\frac{\Delta v}{v} = \frac{\Delta f}{f} + \frac{\Delta \lambda}{\lambda}

. Converting each term to percentage gives

2.0\% + 2.0\% = 4.0\%

Step-by-Step Solution

Calculate the percentage error in the frequency measurement.

\frac{4\text{ Hz}}{200\text{ Hz}} \times 100\% = 2.0\%

Percentage error of a measurement is given by

\frac{\text{absolute error}}{\text{measured value}} \times 100\%

Calculate the percentage error in the wavelength measurement.

\frac{0.01\text{ m}}{0.50\text{ m}} \times 100\% = 2.0\%

The relative uncertainty of the wavelength must be expressed as a percentage.

Sum the individual percentage errors to find the total maximum percentage error for

v = f\lambda

2.0\% + 2.0\% = 4.0\%

When physical quantities are multiplied together, their maximum percentage errors add up.

Key Concept

Propagation of Errors in Products

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