Question

What length should an oboe have to produce a fundamental frequency of 110 Hz on a day when the speed of sound is 343 m/s? It is open at both ends.

a) 1.56 m
b) 0.78 m
c) 3.44 m
d) 0.39 m

Answer 1

The length of the oboe required to produce a fundamental frequency of 110 Hz is 1.56 m.

Step-by-step explanation:

To find the length of the oboe required to produce a fundamental frequency of 110 Hz, we can use the formula for the fundamental frequency of a pipe that is open at both ends. The formula is:

f = (nv) / (2L)

Where f is the frequency, n is the harmonic number (in this case, 1 for the fundamental frequency), v is the velocity of sound, and L is the length of the pipe.

Rearranging the formula, we get:

L = (nv) / (2f)

Substituting the given values, n = 1, v = 343 m/s, and f = 110 Hz, we can calculate the length:

L = (1 * 343) / (2 * 110) = 1.56 m

Therefore, the correct answer is 1.56 m (option a).