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QUESTION: 1

A node is a point where there is always

Solution:

A node is a point along the medium of no displacement. The point is not displaced because destructive interference occurs at this point.

QUESTION: 2

A cylindrical tube, open at both ends, has a fundamental frequency f in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now:

Solution:

As we know, f=v/2l

Now, it will act as one end and one end closed.

So, f_{0}=v/2l’=v/4½=v/2l=f

QUESTION: 3

Fundamental note in open pipe (v_{1 }= ν/2L) has _________ the frequency of the fundamental note in closed organ pipe (v_{2 }= ν/4L).

Solution:

Let L be a length of the pipe,

The fundamental frequency of closed pipe is

v_{2}=ν/4L .....(i)

where ν is the speed of sound in air.

Fundamental frequency of open pipe of same length is

v_{1}=ν/2L .....(ii)

After dividing v_{1} with v_{2},

v_{1}/v_{2}= ν/2L/ ν/4L

v_{1}=2v_{2}

QUESTION: 4

Equation of longitudinal stationary waves in the pipe is

Solution:

QUESTION: 5

In an experiment to find the speed of waves in a rope, a standing wave pattern is established as shown in diagram below. The vibrating end of rope makes 90 vibrations per minute. The speed of the waves is

Solution:

If there are exactly 90 vibrations in 60.0 seconds, then there is a frequency of 1.5 Hz. The diagram shows 1.5 waves in 6.0-meters of rope; thus, the wavelength is 4.0 meters. Now use the equation v=f*w to calculate the speed of the wave. Proper substitution yields 6.0 m/s.

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