In the experiment Standing Waves,if you continue to lwer the water level after recording l(m) at the first sound resonance at fixed tuning fork frequency, you will hear the sound again but sound gets louder (second resonance). At this point, by what factor has l(m) increased? Why?
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To determine the factor by which the wavelength (l) has increased at the second resonance, we need to understand the concept of standing waves and how they relate to the water level.
In this experiment, standing waves are created in the water by using a tuning fork. As you lower the water level, the length of the standing wave changes, which affects the resonance of the sound produced by the tuning fork.
When the water level is adjusted to create the first sound resonance, the standing wave pattern aligns with the tuning fork's frequency. At this point, the length of the standing wave (l₁) is recorded.
To understand why the sound gets louder at the second resonance, we need to know that the intensity of sound waves is proportional to the square of the amplitude of the wave. When the length of the standing wave changes, it affects the amplitude of the wave, which in turn affects the intensity of the sound.
As you continue to lower the water level after the first resonance, you will eventually reach the second resonance, where the sound becomes louder. At this point, the length of the standing wave (l₂) is different from the initial length (l₁).
The factor by which l has increased can be determined by comparing the lengths of the standing waves at both resonances. So the increase in l can be calculated as:
Factor = l₂ / l₁
To measure this increase, you would need to record the length of the standing wave (l(m)) at both the first and second resonances and then divide the length at the second resonance by the length at the first resonance.
By analyzing this factor, you can determine how the change in water level affects the length of the standing wave and subsequently the intensity of the sound produced.