Question

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. What is the length of this pipe? Answer in units of cm.

Answer 1

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.

$\text{Wave speed}=\text{Frequency}\times \text{Wave length}$

$331\frac{\text{m}}{\text{s}}=320\text{ Hz}\times \text{Wave length}$

We know that Hz is equal to $\frac{1}{s}$.

$331\frac{\text{m}}{\text{s}}=320\frac{1}{\text{s}}\times \text{Wave length}$

$331\text{ m}=320\times \text{Wave length}$

$\text{Wave length}=\frac{331}{320}\text{ m}$

$\text{Wave length}=1.034375\text{ m}$

Length of the pipe would be half of the wave-length.

$\text{Length of pipe}=\frac{1.034375}{2}\text{ m}=0.5171875\text{ m}$

Since the length of pipe is in meters, so we will convert it into cm.

1 m = 100 cm

$\text{0.5171875 m}=0.5171875\times 100\text{ cm}=51.71875\text{ cm}\approx 51.72\text{ cm}$

Therefore, the length of the pipe would be 51.72 cm.