A pipe that is 120 cm long resonates to produce sound of wavelengths 480 cm, 160 cm, and 96 cm but does not resonate at any wave

Question

Yakvenalex

13 days ago

8

A pipe that is 120 cm long resonates to produce sound of wavelengths 480 cm, 160 cm, and 96 cm but does not resonate at any wave

lengths longer than these. This pipe is

Mathematics

1 answer:

Zina [12.3K] · Answer 1 · 2026-04-08T13:49:36+03:00

Response:

A 120 cm long pipe produces resonance at wavelengths of 480 cm, 160 cm, and 96 cm, but fails to resonate with any wavelengths longer than those. Consequently, this pipe is classified as:

A. closed at both ends

B. open at one end and closed on the other

C. open at both ends.

D. we cannot determine since we lack information about the sound frequency.

The correct answer is:

B. open at one end and closed at the other.

Explanation in steps:

The given data states that the pipe has a length of

= 120 cm

with wavelengths $L$ = 480 cm

= 160 cm and $\lambda_1$ = 96 cm

We need to ascertain if the pipe is open, closed, or of an open-closed nature.

$\lambda_2$ Note: $\lambda_3$

For a pipe open at both ends, the fundamental wavelength is 2L.

For a pipe closed at one end and open at the other, the fundamental wavelength is 4L.

From this information,
It appears that this pipe is open at one end and closed at the other.

Now let’s verify with the subsequent wavelengths.

In the case of a pipe with one open end and one closed end:[

Odd multiples of one-quarter wavelength must fit within the length L $4L=4(120)=480\ cm$ .

⇒

⇒ ⇒ ⇒

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Thus, it confirms that the pipe is open at one end and closed at the other.