# How Does the Wavelength Change at the Fourth Resonance in a Closed Air Column?

• hamza2095
In summary, the wavelength at 4th resonance is 1.5m, which is 7 times longer than the wavelength at first resonance due to 7/4 of the wave fitting in the 4th resonance. Drawing diagrams can be helpful in solving these types of problems.
hamza2095

## Homework Statement

The resonant length of a closed air column at the first resonance is 0.375m, what is the wavelength when at 4th reasonance

## The Attempt at a Solution

1/4λ=0.375m
λ=1.5m
1.5m/7 = 0.214m

Merlin3189
TSny said:
This was a question on a test, the way I got the answer was knowing v/f=λ and i knew that 7/4 of the wave fits in the 4th reasonance and 1/4 in the first, meaning the frequency is 7x more. I assumed the the velocity was 1.5m/s and the frequency was 1hz so 1.5ms/1hz = 1.5m, after that i mutliplied the 1 hz by 7 to get the answer. Is there an easier way to go about this?, I had trouble with it because the neither the speed of sound or frequency was given.

hamza2095 said:
i knew that 7/4 of the wave fits in the 4th reasonance
That's the key.

Note that the 0.375 m given in the problem represents the length of the pipe. So 7/4 λ = 0.375 m.

You don't need to assume a value for f.

Merlin3189
Ohhh okay I see, thank you. I knew there was an easier way to look at it.

Good. Drawing pictures for these types of problems is always a good thing to do.

Absolutely agree with TSny, draw diagrams. I did.

You may notice my first post is oddly worded, because you tricked me into thinking you'd done the second part wrongly and I had to edit it!
I had ##\frac{λ_1}{4}=0.375## and ##\frac{7λ_2}{4}=0.375## so when I saw your /7 I thought at first you'd missed out the 4.

## 1. What is the definition of "Length of a Closed Air Column"?

The length of a closed air column refers to the distance between the closed end and the open end of the air column, where sound waves can travel and resonate.

## 2. How does the length of a closed air column affect the pitch of a sound?

The length of a closed air column directly affects the pitch of a sound. A shorter air column will produce a higher pitch, while a longer air column will produce a lower pitch.

## 3. What is the relationship between the length of a closed air column and the wavelength of a sound wave?

The length of a closed air column and the wavelength of a sound wave are inversely proportional. This means that as the length of the air column increases, the wavelength of the sound wave decreases, and vice versa.

## 4. How does the length of a closed air column impact the speed of sound?

The length of a closed air column has no direct impact on the speed of sound. However, it can indirectly affect the speed of sound by changing the frequency and wavelength of the sound wave.

## 5. How can the length of a closed air column be changed?

The length of a closed air column can be changed by physically altering the length of the column, such as by adjusting the length of a wind instrument or changing the size of a closed space. It can also be changed by changing the temperature or pressure of the air column.

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