Resonance in a system, such as a string fixed at both ends, occurs when
a) it is oscillating in simpler harmonic motion
b) its frequency is the same as the frequency of an external source
c) its frequency is greater than the frequency of an external source
d) its frequency is smaller that the frequency of an external source
well, I don't like b,c,d. I would have worded it as "natural frequency" is ...
Assuming the author meant that, then b makes perfect sense.
Am I nitpicking? No. The frequency observed will always be the same as the external source. Duh. Resonance is when the external source is tuned to the natural frequency of the object.
c) its frequency is greater than the frequency of an external source
The correct answer is b) its frequency is the same as the frequency of an external source.
When a system, such as a string fixed at both ends, is in resonance with an external source, it means that the natural frequency of the system matches the frequency of the external source.
To understand this concept, let's break it down step by step:
1. Natural Frequency: Every physical system has a natural frequency, which is the frequency at which it naturally tends to vibrate or oscillate when disturbed. For example, a guitar string has a natural frequency at which it vibrates when plucked.
2. External Source: An external source refers to any force or input that can induce vibrations in the system. In the case of a string fixed at both ends, an external source could be another string or an instrument that produces sound waves.
3. Resonance: When the frequency of the external source matches the natural frequency of the system, resonance occurs. This means that the system responds strongly to the external source, resulting in a larger amplitude of vibrations. In the case of the string, it would vibrate with a larger amplitude when the frequency of the external source matches its natural frequency.
So, the correct answer is b) its frequency is the same as the frequency of an external source because resonance occurs when the frequencies are matching.