A sound wave traveling through air at a constant temperature has a frequency of 250\text{ … — Armed Services Vocational Aptitude Battery (ASVAB)

A sound wave traveling through air at a constant temperature has a frequency of $250\text{ Hz}$ and a wavelength of $1.36\text{ m}$ . If the frequency of the sound source increases to $500\text{ Hz}$ , what is the new wavelength of the sound wave?

A
$2.72\text{ m}$
B
$1.36\text{ m}$
$0.68\text{ m}$ Answer
D
$0.34\text{ m}$

Answer

The new wavelength is

0.68\text{ m}

Wave speed in a given medium at constant temperature is constant (

v = f\lambda

). The initial speed is

250\text{ Hz} \times 1.36\text{ m} = 340\text{ m/s}

. When the frequency doubles to

500\text{ Hz}

, the wavelength must be halved:

340\text{ m/s} \div 500\text{ Hz} = 0.68\text{ m}

Step-by-Step Solution

Calculate the constant wave speed in air using the initial conditions

v = f_1 \times \lambda_1 = 250\text{ Hz} \times 1.36\text{ m} = 340\text{ m/s}

The speed of a mechanical wave depends entirely on the medium and remains constant at a fixed temperature.

Rearrange the wave equation to solve for the new wavelength

\lambda_2 = \frac{v}{f_2} = \frac{340\text{ m/s}}{500\text{ Hz}} = 0.68\text{ m}

Because wave speed is constant, an increase in frequency causes an inversely proportional decrease in wavelength.

Key Concept

Inverse relationship between frequency and wavelength in a constant medium (

v = f\lambda

)

Estimated Time:1m 0s

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