Answer:
51.72 cm.
Step-by-step explanation:
We have been given that a pipe that is open at both ends has a fundamental frequency of 320 Hz when the speed of sound in air is 331 m/s. We are asked to find the length of the pipe.
First of all, we will find the wavelength using following formula.
[tex]\text{Wave speed}=\text{Frequency}\times \text{Wave length}[/tex]
[tex]331\frac{\text{m}}{\text{s}}=320\text{ Hz}\times \text{Wave length}[/tex]
We know that Hz is equal to [tex]\frac{1}{s}[/tex].
[tex]331\frac{\text{m}}{\text{s}}=320\frac{1}{\text{s}}\times \text{Wave length}[/tex]
[tex]331\text{ m}=320\times \text{Wave length}[/tex]
[tex]\text{Wave length}=\frac{331}{320}\text{ m}[/tex]
[tex]\text{Wave length}=1.034375\text{ m}[/tex]
Length of the pipe would be half of the wave-length.
[tex]\text{Length of pipe}=\frac{1.034375}{2}\text{ m}=0.5171875\text{ m}[/tex]
Since the length of pipe is in meters, so we will convert it into cm.
1 m = 100 cm
[tex]\text{0.5171875 m}=0.5171875\times 100\text{ cm}=51.71875\text{ cm}\approx 51.72\text{ cm}[/tex]
Therefore, the length of the pipe would be 51.72 cm.
