Question 289: Waves

Question

A pipe 60 cm long and open at both the ends produces harmonics. Which harmonic mode of pipe resonates a 2.2 KHz source?
(Speed of sound in air $=330 \mathrm{~m} / \mathrm{s})($ Neglect end correction)

Accepted Answer

Given:
Length of pipe, $ l = 60 \, 	ext{cm} $
Frequency of the source, $ f = 2200 \, 	ext{Hz} $
Speed of sound, $ v = 330 \, 	ext{m/s} $
To find which harmonic mode of the pipe resonates with a 2.2 kHz source in an open pipe, we use the formula for the frequency of the $ n $-th harmonic:
$ f = n \cdot \frac{v}{2l} $
Substituting the given values:
$ 2200 = n \left(\frac{330}{2 	imes 0.60}ight) $
Simplifying the equation:
$ 2200 = n \left(\frac{330}{1.2}ight) $
$ 2200 = n 	imes 275 $
Solving for $ n $:
$ n = \frac{2200}{275} $
$ n = 8 $
Thus, the pipe resonates with the eighth harmonic mode.

Answer

First

Answer

Eighth

Answer

Third

Answer

Second

Waves

A pipe 60 cm long and open at both the ends produces harmonics. Which harmonic mode of pipe resonates a 2.2 KHz source? (Speed of sound in air =330 \mathrm{~m} / \mathrm{s})( Neglect end correction)

Choose the correct answer: