If an open organ pipe of length 20 cm resonates with 1 khz, in the third harmonic mode, find the wave length of the standing wave produced .

Explanation

Let l = length of an open organ pipe. For the funda-mental mode of vibration, as shown in the Fig. 4.24 (a), the wavelengths `lambda` is such that,
` l = (lambda)/(2) or, lambda = 2l`
Now, `V = n lambda , or, nlambda ` = constant, as the velocity of sound is constant.
` :.lambda prop (1)/(n)`
An open pipe produces all the overtones. So the frequency of the 3rd harmonic would be three times that of the fundamental. Then the wavelength would be one-third . For the fundamental. We already have, ` lambda = 2l` .
Soo, for the 3rd harmonic,
wavelength ` = (2l)/(3) = (2 xx 20)/(3) = 13 . 3 ` cm
[From the resonance condition, frequency = 100 Hz., `:. V = nlambda = 1000 xx 13 . 3 = 13300 cm *s^(-1) = 133 m*s^(-1)` This is not correct value of V, it should be `330 m*s^(-1)` , incorrect date has been given . ]