Question

A vibrating diaphragm sets up strong vibrations at the mouth of a horizontal tube containing air and a small amount of fine powder. The powder becomes arranged in piles 1 centimeter apart. Assume the speed of sound in air to be 330 meters per second.

1) The wavelength of this sound in air is?

Answer 1

Will the powder occur at the nodes or antinodes or what?
just explain the powder part.

Answer 2

You want answer to ^^ with respect to pressure wave or displacement wave ??

Answer 3

The powder will accumulate where pressure is lowest, since powder is easily dispersed. These these would be the nodes. These nodes occur twice per period, because sine waves go through zero twice each period.

Twice the distance between a node is the wavelength.

If Sound travels 330 meters/sec and the distance between nodes is .01 meters, then the sound wave will repeat every .02/330 seconds: 60.6 microseconds. This corresponds to a frequency of 16.5 kHz, which is within the possible hearing range of humans.

Answer 4

@ybarrap
I think we can consider powder as suspended particles and hence treat them like air molecules. Therefore they will be at points of highest pressure.

Although it won't change anything as the distance between two nodes and antinodes is same. (Unless the question specifically ask for it)

Answer 5

I agree.

Answer 6

I think I need the answer in displacement wave.

Answer 7

@shayanreloaded
What's the phase difference b/w pressure wave and displacement wave ??

Answer 8

I don't know what a pressure wave is..

Answer 9

Where the powder sits is where the amplitude of the displacement is zero.
These nodal points are spaced by \(\lambda /2\) which allows you to conclude that \(\lambda\) = 2 cm.