Which of the following situations is a result of resonance?
a. Hydro wires "hum" as a mild breeze blows over them.
b. A child pushes herself on a swing by moving her legs back and forth appropriately.
c. Windows in your house rattle as a large truck drives by.
d. Buildings begin to sway when an earthquake occurs.
e. all of the above
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The correct answer is e. all of the above. Resonance occurs when an object or system vibrates at its natural frequency due to the external force matching that frequency. In each of the given situations, resonance is involved.
a. When a mild breeze blows over hydro wires, they can vibrate at their natural frequency, resulting in a humming sound.
b. When a child pushes herself on a swing, she builds up the swinging motion by applying force at the right frequency, matching the swing's natural frequency.
c. When a large truck drives by, it can generate vibrations that match the natural frequency of the windows, causing them to rattle.
d. In an earthquake, the ground shakes at various frequencies, and if the natural frequency of a building matches one of those frequencies, the building can begin to sway due to resonance.
To determine which of the situations is a result of resonance, we need to understand what resonance is and apply the concept to each situation.
Resonance refers to the tendency of an object or system to vibrate with increased amplitude when exposed to a periodic force or frequency that matches its natural frequency. This occurs when the driving frequency matches the resonant frequency of the system, causing it to absorb and store energy, resulting in a significant response.
Now, let's analyze each situation:
a. Hydro wires "hum" as a mild breeze blows over them.
In this case, the mild breeze creates air pressure fluctuations that can excite the natural frequency of the hydro wires, causing them to vibrate with a larger amplitude. This is a result of resonance.
b. A child pushes herself on a swing by moving her legs back and forth appropriately.
The swinging motion of the child occurs due to the interaction between the periodic force applied by the child and the natural frequency of the swing. However, this is not an example of resonance because the child is continuously exerting force to maintain and increase the amplitude of the swing's motion.
c. Windows in your house rattle as a large truck drives by.
When a large truck drives by, it produces vibrations and sound waves that can match the natural frequency of the windows, causing them to rattle. This is an example of resonance since the vibrations from the truck's movement excite the natural frequency of the windows.
d. Buildings begin to sway when an earthquake occurs.
During an earthquake, the ground shakes with various frequencies. If the frequency of the shaking matches the natural frequency of a building, resonance can occur. The building absorbs and amplifies the energy, causing it to sway significantly. Therefore, this is also an example of resonance.
Based on the analysis of each situation, the correct answer is e. All of the above. Both situations a and c demonstrate resonance, while situations b and d do not.