The amplitude of a standing sound wave in a long pipe closed at the left end is

Question

The amplitude of a standing sound wave in a long pipe closed at the left end is sketched below The vertical axis is the maximum displacement of the air, and the horizontal axis is along the length of the pipe. What is the harmonic number for the mode of oscillation illustrated? 3 ou are e re158-43ihrequeny) f the oundl Use 340 mlj or hef sound in ar Previous Tries Your receipt no. is 158-6315 The length of the pipe is 0.440 m. What is the pitch (frequency) of the sound? Use 340 m/s for the speed of sound in air. 1160 Hz The harmonic number of a mode is qiven by the ratio of the frequency of the mode to that of the fundamental mode. From the harmonic number you can get the wavelength and then the frequency Submit Answer Incorrect. Tries 2/20 Previous Tries The pipe is now held vertically, and a small amount of water is poured inside the pipe. The first harmonic frequency is then measured to be 220.2 Hz Measuring from the bottom of the pipe, what is the level of the water? Submit Answer Tries 0/20

Explanation / Answer

Solution- b) We know that
frequency=speed/wavelength
here length of pipe=3/4 * wavelength
wavelength=0.44/(3/4)=0.59 m
so frequency=340/0.58=586.21 Hz

c)Now for the first harmonic,
pipe length=(1/4)* wavelength
wavelength=4*pipe length
Again the frequency=speed/wavelength
220.0=340/wavelength
wavelength=340/220.0=1.54 m
therefore the pipe length=1.54/4=0.385 m
Hence the level of water=0.44-0.385=0.055 m

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