Suppose a piano tuner hears 2 beats per second when listening to the combined sound from her tuning fork and the piano note being tuned. After slightly tightening the string, she hears 1 beat per second. Should she loosen or continue to further tighten the string? Why?
She should continue to tighten the string, because tightening the string but her closer to the correct frequency.
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Based on the given information, the piano tuner hears 2 beats per second when both the tuning fork and the piano note are sounding. After slightly tightening the string, she hears 1 beat per second.
To determine whether she should loosen or continue to tighten the string, we need to understand the concept of beats in the context of tuning.
Beats occur when two sounds with slightly different frequencies are played together. The number of beats per second is directly related to the difference in frequency between the two sounds. If the frequency difference is larger, the beats will be faster, and if the frequency difference is smaller, the beats will be slower.
In this case, the tuner hears fewer beats per second after tightening the string. This implies that the frequencies of the tuning fork and the piano note are now closer together.
Since tightening the string decreased the frequency difference, the tuner should continue to further tighten the string. This will minimize the frequency difference between the tuning fork and the piano note, eventually resulting in no beats being heard. At that point, the note will be in tune with the tuning fork.
Therefore, the tuner should continue to further tighten the string.
To determine whether the piano tuner should loosen or continue to further tighten the string, we need to understand the concept of beats in terms of the piano's tuning.
Beats occur when two sound waves with slightly different frequencies interfere with each other. In this scenario, the piano tuner is using a tuning fork, which produces a known frequency, and comparing it with the frequency of the piano string being tuned.
In the initial situation, the tuner hears 2 beats per second. This indicates that the frequency of the piano string is slightly higher than the tuning fork's frequency. By tightening the string, the tuner is attempting to increase its tension and thus its frequency.
After tightening the string, the tuner now hears 1 beat per second. This suggests that the frequency of the piano string is becoming closer to the tuning fork's frequency. However, it's important to note that the string still has a higher frequency, as evidenced by the presence of beats.
To resolve the beats and achieve a proper tuning, the tuner should continue to further tighten the string. By doing so, the tension of the string is increased, causing its frequency to rise. As the string's frequency reaches and matches the tuning fork's frequency, the beats will disappear, indicating that the piano string is in tune.
In summary, the piano tuner should continue to further tighten the string to eliminate the presence of beats and achieve the desired tuning.