A string is stretched so that it is under tension and is tied at both ends so that the endpoints don't move. A mechanical oscillator then vibrates the string so that a standing wave is created. The dark line in each diagram represents a snapshot of a string at an instant in time when the amplitude of the standing wave is a maximum. The lighter lines represent the string at other times during a complete cycle. All of the strings are identical except for their lengths, and all strings have the same tension. The number of nodes and antinodes in each standing wave is different. the lengths of the strings (L) and the amplitudes at the antinodes (A) are given in each figure.
Rank the speed of the wave in the strings.
Enter in the form A > B = C .
Hint: v=(T/μ)0.5.
Transcribed Image Text:### The Effect of Tension and Frequency on Wave Patterns
The image displays four different wave patterns labeled A, B, C, and D, each related to varying tension (T) in Newtons (N) and frequency (f) in Hertz (Hz).
#### A) T = 2 N, f = 500 Hz
This graph shows a wave with lower amplitude and higher frequency. The waves are closely packed with several cycles occurring within a given length, indicating a high frequency of 500 Hz under a tension of 2 Newtons.
#### B) T = 5 N, f = 300 Hz
In contrast, this graph shows a wave under higher tension of 5 Newtons with a frequency of 300 Hz. The wave pattern is less dense compared to A, marking fewer oscillations within the same length, corresponding to a lower frequency.
#### C) T = 6 N, f = 300 Hz
Here, the wave is under the highest tension of 6 Newtons but still maintains the same frequency of 300 Hz as in B. The wave appears even less dense, showing fewer oscillations compared to A and B. The increased tension creates a wave that appears more spread out and elongates the wavelength.
#### D) T = 2 N, f = 400 Hz
This graph shows a wave pattern under the same tension as A (2 Newtons) but with a frequency of 400 Hz. The wave pattern falls between A and B in terms of density, indicating a frequency higher than B but lower than A.
### Overall Observations
- **Tension Impact**: As tension increases, the wave appears more stretched out, creating fewer oscillations in a given length and altering the wavelength.
- **Frequency Impact**: Higher frequencies result in waves that are more densely packed with more oscillations in the same length, and lower frequencies create more elongated waves.
Through this illustration, we see the combined influence of tension and frequency on wave formation, crucial for understanding wave behaviors in different physical contexts.
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