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

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.

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7 months 2021-10-08T17:36:01+00:00 1 Answer 0 views 0

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.