A boat is floating on still water.
2 answers:
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The frequency of the nth-harmonic of a string is given by
where n is the number of the harmonic, L is the length of the string, T the tension and
the linear density.
In our problem, since the mass m is tied to the string, the tension is equal to the weight of the object tied:
Substituting into the first formula, we have
In our problem we have n=2 (second harmonic). In the previous equation, the only factor which is not constant between the first and the second part of the problem is m, the mass. So, we can rewrite everything as
where we called
In the first part of the problem, the mass of the object is m and
. So we can write
When the mass is increased with an additional 1.2 kg, the relationship becomes
By writing K in terms of m in the first equation, and subsituting into the second one, we get
and solving this, we find
where n is the number of the harmonic, L is the length of the string, T the tension and
In our problem, since the mass m is tied to the string, the tension is equal to the weight of the object tied:
Substituting into the first formula, we have
In our problem we have n=2 (second harmonic). In the previous equation, the only factor which is not constant between the first and the second part of the problem is m, the mass. So, we can rewrite everything as
where we called
In the first part of the problem, the mass of the object is m and
When the mass is increased with an additional 1.2 kg, the relationship becomes
By writing K in terms of m in the first equation, and subsituting into the second one, we get
and solving this, we find