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Elis [28]
3 years ago
13

A string fixed at both ends has a length of 1 m. With a frequency of 44 kHz (fourth overtone), standing waves are produced. Whic

h harmonics will be audible to a human? (The frequency range for human hearing is 20 Hz to 20 kHz)
Physics
1 answer:
Taya2010 [7]3 years ago
6 0
The frequency of the nth-harmonic of a standing wave is an integer multiple of the fundamental frequency of the string, according to:
f_n = nf_1 (1)
where f_1 is the fundamental frequency.

We know the frequency of the 4th overtone (44 kHz), which corresponds to the 5th harmonic (n=5). Therefore, we can find the fundamental frequency of the string by rearranging equation (1):
f_1 =  \frac{f_5}{5}= \frac{44 kHz}{5}=8.8 kHz

And by using the same formula we can find the following harmonics:
f_2 = 2 f_1 = 2 \cdot 8.8 kHz =17.6 kHz
f_3 = 3f_1 = 3 \cdot 8.8 kHz =26.4 kHz
f_4 = 4 f_1 = 4 \cdot 8.8 kHz =35.2 kHz

And since the audible range for human goes from 20 Hz to 20 kHz, we see that onlyt the first two harmonics (8.8 kHz and 17.6 kHz) will be audible to a human.
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