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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Sound Waves

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Sound Waves

A person is able to hear sound waves within the frequency range of...

A person is able to hear sound waves within the frequency range of 20 Hz20 \text{ Hz} to 20 kHz20 \text{ kHz}. Determine the minimum and maximum wavelengths of sound audible to the person. Assume the speed of sound is 360 m s−1360 \text{ m s}^{-1}.

Options

  1. A18 cm18 \text{ cm} and 180 m180 \text{ m}
  2. B1.8 mm1.8 \text{ mm} and 1.8 m1.8 \text{ m}
  3. C18 mm18 \text{ mm} and 18 m18 \text{ m}
  4. D18 m18 \text{ m} and 18 mm18 \text{ mm}

Correct answer

C. 18 mm18 \text{ mm} and 18 m18 \text{ m}

Step-by-step solution

Given, speed of sound, v=360 m s−1v = 360 \text{ m s}^{-1}

Minimum frequency, f_\min = 20 \text{ Hz}

Maximum frequency, f_\max = 20 \text{ kHz} = 20000 \text{ Hz}

The relation between speed, frequency, and wavelength is given by v=fλ⇒λ=vfv = f \lambda \Rightarrow \lambda = \dfrac{v}{f}

For minimum wavelength, frequency must be maximum:

\lambda_\min = \dfrac{v}{f_\max} = \dfrac{360}{20000} = 18 \times 10^{-3} \text{ m} = 18 \text{ mm}

For maximum wavelength, frequency must be minimum:

\lambda_\max = \dfrac{v}{f_\min} = \dfrac{360}{20} = 18 \text{ m}

Thus, the minimum and maximum wavelengths are 18 mm18 \text{ mm} and 18 m18 \text{ m} respectively.
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