A 1.5-m string is held fixed at both ends. When driven by a 180-Hz source, the string vibrates in 3 distinct segments. What is the natural fundamental frequency of the string?Select one:a.60 Hzb.30 Hzc.90 Hzd.540 Hz
Question
A 1.5-m string is held fixed at both ends. When driven by a 180-Hz source, the string vibrates in 3 distinct segments. What is the natural fundamental frequency of the string?Select one:a.60 Hzb.30 Hzc.90 Hzd.540 Hz
Solution
The natural fundamental frequency of a string is the lowest frequency at which it vibrates. This is also known as the first harmonic.
In this case, the string is vibrating in 3 distinct segments when driven by a 180-Hz source. This means that the 180-Hz frequency is the third harmonic of the string (since the third harmonic corresponds to the string vibrating in 3 segments).
The fundamental frequency (or first harmonic) is therefore one third of the third harmonic.
So, to find the fundamental frequency, we divide the third harmonic frequency by 3:
180 Hz / 3 = 60 Hz
So, the natural fundamental frequency of the string is 60 Hz.
Therefore, the correct answer is a. 60 Hz.
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