A 524-Hz longitudinal wave in air has a speed of 345 m/s. (a) What is the wavelength? (b) How much time is required for the phase to change by 90° at a given point in space? (c) At a particular instant, what is the phase difference (in degrees) between two points 4.4 cm apart?

a) 152 cm

b) 0.725 ms

c) 10°

Explanation:

Given

Frequency of the wave, f = 524 Hz

Speed of the wave, v = 345 m/s

Wavelength of the wave, λ = ?

The relation for wavelength is given by

λ = f/v, on substituting

λ = 524 / 345

λ = 1.52 m or 152 cm

T = 1/v

T = 0.0029 s

T = 2.9 ms.

Note that the phase change is 90°, thus the time required to change the phase by 90° is

t = 2.9 * (90 / 360)

t = 2.9 * 0.25

t = 0.725 ms

The phase difference at a particular instance 4.4 cm apart is

= (4.4 / 152) * 360

= 0.02895 * 360

= 10.422°

a) 152 cm

b) 0.725 ms

c) 10°

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