Waves and its Characteristics

Practice Questions:

Question 31: easy

Which of the following equations represents a progressive harmonic wave travelling along y-axis? (All symbols have their usual meaning)

1. \(y = A sin(kx - \omega t)\)

2. \(y = A sin kz cos 2\pi t\)

3. \(x = A sin(ky - \omega t)\)

4. \(x = A sin(kz + \omega t)\)

View Answer

A progressive wave along the y-axis must have a phase containing the term \((ky \pm \omega t)\). Thus, \(x = A sin(ky - \omega t)\) represents a transverse wave travelling along the y-axis.

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Question 32: easy

A progressive wave of frequency \(500\text{ Hz}\) is travelling with a speed of \(330\text{ m/s}\) in air. The distance between the two points which have a phase difference \(30^{circ}\) is

1. 0.11 m

2. 0.055 m

3. 0.22 m

4. 0.025 m

View Answer

Wavelength \(\lambda = \frac{v}{f} = \frac{330}{500} = 0.66\text{ m}\). Path difference \(\Delta x = \frac{\lambda}{2\pi} \Delta \phi = \frac{0.66}{2\pi} \left(\frac{\pi}{6}\right) = 0.055\text{ m}\).

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