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Andre45
1 month ago
12

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 phas

e 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?
Physics
1 answer:
serg [3.5K]1 month ago
5 0
a) 152 cm, b) 0.725 ms, c) 10°. The frequency of the wave is 524 Hz, and its speed is 345 m/s. The wavelength (λ) can be found using the formula λ = f/v; thus, λ = 524 / 345 results in 1.52 m or 152 cm. The period (T) is calculated as T = 1/v, yielding T = 0.0029 s or 2.9 ms. The phase change is noted at 90°, so the time to change the phase by 90° at a location is t = 2.9 * (90 / 360) = 0.725 ms. For two points separated by 4.4 cm, the phase difference at that instance calculates to about 10°.
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A resultant vector is 8.00 units long and makes an angle of 43.0 degrees measured ������� – ��������� with respect to the positi
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223 degrees

Explanation:

We have the following information:

Magnitude of the resultant vector = 8 units

The resultant vector makes a counterclockwise angle with the positive x-axis

\theta=43^{\circ}

Our goal is to determine the magnitude and angle of the equilibriant vector.

We understand that the equilibrium vector has the same magnitude but is oriented in the opposite direction of the given vector.

Thus, the equilibrium vector's magnitude = 8 units

x-component of a vector=v_x=vcos\theta

Where v = Magnitude of vector

Using the formula:

x-component of the resultant vector=v_x=8cos43=5.85

y-component of the resultant vector=v_y=vsin\theta=8sin43=5.46

x-component of the equilibrium vector=v_x=-5.85

y-component of the equilibrium vector=-v_y=-5.46

Because the equilibrium vector lies in the third quadrant

\theta=tan^{-1}(\frac{v_x}{v_y})=tan^{-1}(\frac{-5.46}{-5.85})=43^{\circ}

The angle \theta' is in the third quadrant

In the third quadrant, the angle =\theta'+180^{\circ}

The angle of the equilibrium vector measured from the positive x-axis in a counterclockwise direction is 180+43=223 degrees

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