Question

You run toward an open pipe resonating at its fundamental frequency at a speed of 15 m/s, and you hear the frequency as 214 Hz. How long is the pipe?

a) 1.5 m
b) 2 m
c) 3 m
d) 4 m

Answer 1

To find the length of the pipe resonating at its fundamental frequency, you can use the formula λ = v / f, where λ is the wavelength, v is the speed of sound, and f is the frequency. Given that the speed of sound is 331 m/s and the frequency is 214 Hz, the length of the pipe is approximately 0.77 m.

Step-by-step explanation:

To find the length of the pipe resonating at its fundamental frequency, we can use the formula:

λ = v / f

Where λ is the wavelength, v is the speed of sound, and f is the frequency.

Given that the speed of sound is 331 m/s and the frequency is 214 Hz, we can plug in these values to calculate the wavelength:

λ = 331 m/s / 214 Hz = 1.545 m

Since the pipe is open at both ends, we can use the formula:

L = λ / 2

Plugging in the calculated wavelength, we find:

L = 1.545 m / 2 = 0.7725 m

Therefore, the length of the pipe is approximately 0.77 m.