Question

1-state the relationship between a wave's velocity wavelength and frequency?

2- What is the principle of superposition?

3- The distance between two nodes or two antinodes in a standing wave is …………………. Wavelength?

4- - The distance between an antinode and a node in a standing wave is …………………. Wavelength?

5- A string, which has a mass of 0.50 kg and a length of 3.0 meters, is clamped on both ends. If the tension in the string is 25 Newtons, what are the lowest 3 natural frequencies of oscillation of the string? For each case, include a sketch of the standing wave pattern.

Answer 1

1 . Wavelength = Speed / frequency

The higher the frequency, the shorter the wavelength.

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2. The principle of superposition may be applied to waves whenever two (or more) waves travelling through the same medium at the same time. The waves pass through each other without being disturbed. The net displacement of the medium at any point in space or time, is simply the sum of the individual wave displacements

e.g

Two waves (with the same amplitude, frequency, and wavelength) are travelling in the same direction. Using the principle of superposition, the resulting wave displacement may be written as:

y ( x , t ) = y m sin ( kx - ωt ) + y m sin ( kx - ωt + ϕ ) = 2 y m cos ( ϕ / 2 ) sin ( kx - ωt + ϕ / 2 )

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3. The distance between two nodes or two antinodes in a standing wave is half of Wavelength

4. The distance between an antinode and a node in a standing wave is One forth of Wavelength

5. linear density of string = m/L = 0.50 / 3 kg/m

speed of wave = sqrt( T / linear density) = 12.25 m/s

for 1st,

Wavelength = 2L = 6 m

Wavelength = Speed / frequency

6 = 12.25 / frequency

frequency = 2.04 Hz

for 2nd ,

wavelength = L   = 3 m

frequency = 12.25 / 3 = 4.08 Hz

For 3rd ,

1.5* wavelength = L   = 3 m

wavelength = 2 m

Frequency = 1.2.25 / 2 = 6.125 Hz