Question

A flagpole consists of a flexible, 7.14 m tall fiberglass pole planted in concrete. The bottom end of the flagpole is fixed in position, but the top end of the flagpole is free to move. What is the lowest frequency standing wave that can be formed on the flagpole if the wave propagation speed in the fiberglass is 2730 m/s?

Answer 1

Answer:

The lowest frequency is 95.6 Hz

Explanation:

The standing waves that can be formed in this system must meet some conditions, such as until this is fixed at the bottom here there must be a node (point without oscillation) and being free at its top at this point there should be maximum elongation (antinode)

For the lowest frequency we have a node at the bottom point and a maximum at the top point, this corresponds to ¼ of the wavelength, so the full wave has

      λ = 4L

 

As the speed any wave is equal to the product of its frequency by the wavelength

 

      v = f λ

      f = v / λ    

      f = v / 4L

      f = 2730 / (4 7.14)

      f=  95.6 1 / s = 95.6 Hz

Answer 2

The lowest frequency of the standing wave that can be formed on the flagpole is 95.59 Hz.

Data obtained from the question

• Length (L) = 7.14 m
• Wavelength (λ) = 4L = 4 × 7.14 = 28.56 m
• Velocity (v) = 2730 m/s

• Frequency (f) =?

How to determine the frequency

The velocity, frequency and wavelength of a wave are related according to the following equation:

Velocity (v) = wavelength (λ) × frequency (f)

v = λf

With the above formula, we can obtain the frequency as follow:

v = λf

2730 = 28.56 × f

Divide both side by 28..56

f = 2730 / 28.56

f = 95.59 Hz

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