High School

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A wave travels down a string with a velocity of 512 m/s. If the string has a length of 6.84 meters, what is the second harmonic frequency of this string?

A. 37.1 Hz
B. 74.9 Hz
C. 165 Hz
D. 3500 Hz

Answer :

Final answer:

The second harmonic frequency of a string can be calculated using the formula f_n = n(v/2L). Given the velocity of 512 m/s and length of 6.84 meters, the second harmonic frequency is found to be 74.9 Hz, matching option b.

Explanation:

To find the second harmonic frequency of a string, we first need to understand that the frequency of the nth harmonic can be calculated using the formula f_n = n(v/2L), where v is the velocity of the wave, L is the length of the string, and n represents the harmonic number. In this case, the second harmonic (n=2) is in question.

Given that the velocity (v) of the wave is 512 m/s, and the length (L) of the string is 6.84 meters, we can substitute these values into the formula:

f_2 = 2(512 m/s / 2*6.84 m) = 74.9 Hz

Therefore, the second harmonic frequency of this string is 74.9 Hz, which corresponds to option b.

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