Question

As you make your way through the promenade, a calliope starts up Fučik's Entry of the Gladiators. The Calliope functions by blowing steam through a series of pipes open at the top end. 1. You note that the pipe on the far end is 101.60 mm in length. What frequency of notes can it play as it's fundamental and second harmonics? Take the speed of sound in steam to be 477.5 m/s 2.

Answer 1

The fundamental frequency of the calliope pipe is 2354.24 Hz, and the second harmonic has a frequency of 4708.48 Hz.

Step-by-step explanation:

To determine the frequency of the fundamental and second harmonics of a calliope pipe, we can use the formula: f = nv/2L, where f is the frequency, n is the harmonic number (1 for the fundamental frequency and 2 for the second harmonic), v is the speed of sound in steam, and L is the length of the pipe.

For the fundamental frequency (n = 1), the length of the pipe is given as 101.60 mm. We can convert this length to meters by dividing by 1000: L = 101.60 / 1000 = 0.1016 m.

Plugging the values into the formula, we hav: f = (1)(477.5) / (2)(0.1016) = 2354.24 Hz for the fundamental frequency.

For the second harmonic (n = 2), the formula remains the same but with n = 2: f = (2)(477.5) / (2)(0.1016) = 4708.48 Hz for the second harmonic.