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To solve this problem we will apply the concept of wavelength, which warns that this is equivalent to the relationship between the speed of the air (in this case in through the air) and the frequency of that wave. The air is in standard conditions so we have the relation,
Frequency
Speed of sound in air
The definition of wavelength is,
Here,
v = Velocity
f = Frequency
Replacing,
Therefore the wavelength of that tone in air at standard conditions is 0.589m
The acorn was at a height of <u>4.15 m</u> from the ground before it drops.
The acorn takes a time t to fall through a distance h₁, which is the length of the scale. When the acorn reaches the top of the scale, its velocity is u.
Calculate the speed of the acorn at the top of the scale, using the equation of motion,
Since the acorn falls freely under gravity, its acceleration is equal to the acceleration due to gravity g.
Substitute 2.27 m for s (=h₁), 0.301 s for t and 9.8 m/s² for a (=g).
If the acorn starts from rest and reaches a speed of 6.067 m/s at the top of the scale, it would have fallen a distance h₂ to achieve this speed.
Use the equation of motion,
Substitute 6.067 m/s for v, 0 m/s for u, 9.8 m/s² for a (=g) and h₂ for s.
The height h above the ground at which the acorn was is given by,
The acorn was at a height <u>4.15m</u> from the ground before dropping down.