A sound wave having a frequency of 100 Hz is travelling in air. The speed of sound in air is 350 m s^ -1 . What is the phase difference at a given instant between two points separated by a distance of 10.0 cm along the

Correct answer: C. (2π)/(35) Given frequency f = 100 Hz and speed of sound v = 350 m s^ -1 . The wavelength of the sound wave is given by: λ = (v)/(f) = (350)/(100) = 3.5 m The phase difference Δ φ between two points separated by a distance Δ x is: Δ φ = (2π)/(λ) Δ x Given Δ x = 10.0 cm = 0.1 m . Substituting the values: Δ φ = (2π)/(3.5) × 0.1 = (0.2π)/(3.5) = (2π)/(35)

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 sound wave having a frequency of 100 Hz is travelling in air. The...

A sound wave having a frequency of

100 \text{ Hz}

is travelling in air. The speed of sound in air is

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

. What is the phase difference at a given instant between two points separated by a distance of

10.0 \text{ cm}

along the direction of propagation?

Options

A $\dfrac{\pi}{70}$
B $\dfrac{4\pi}{35}$
C $\dfrac{2\pi}{35}$
D $\dfrac{\pi}{35}$

Correct answer

C. $\dfrac{2\pi}{35}$

Step-by-step solution

Given frequency

f = 100 \text{ Hz}

and speed of sound

v = 350 \text{ m s}^{-1}

.

The wavelength of the sound wave is given by:

\lambda = \dfrac{v}{f} = \dfrac{350}{100} = 3.5 \text{ m}

The phase difference

\Delta \phi

between two points separated by a distance

\Delta x

is:

\Delta \phi = \dfrac{2\pi}{\lambda} \Delta x

Given

\Delta x = 10.0 \text{ cm} = 0.1 \text{ m}

. Substituting the values:

\Delta \phi = \dfrac{2\pi}{3.5} \times 0.1 = \dfrac{0.2\pi}{3.5} = \dfrac{2\pi}{35}

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