Question

4. Stan Dinghwaives is playing his open-end pipe. The frequency of the second harmonic is 880

Hz (a pitch of A5). The speed of sound through the pipe is 350 m/sec. Find the frequency of the

first harmonic and the length of the pipe.

Answer 1

The frequency of the first harmonic of the pipe Stan is playing is 440 Hz, and the length of the pipe is approximately 0.398 meters.

Step-by-step explanation:

We need to find the frequency of the first harmonic (fundamental frequency) and the length of the pipe that Stan is playing. The second harmonic of an open-end pipe is twice the frequency of the first harmonic.

Since the frequency of the second harmonic is given as 880 Hz, we can find the frequency of the first harmonic by dividing this by 2:

F1 = 880 Hz / 2 = 440 Hz

Now, for an open pipe, the wavelength (λ) of the first harmonic is twice the length of the pipe (L), and the formula to find the speed of sound (v) is λ × f where f is the frequency. By rearranging this formula, we can find L:

λ = v / f1

λ = 350 m/s / 440 Hz = 0.795 m

Therefore, L = λ / 2 = 0.795 m / 2 = 0.398 m

The pipe has a length of approximately 0.398 meters.