Answer
a) $$ L = 0.328 m$$
b) $$λ = 1.312 m$$
c) $$ f = 262.2 Hz$$
Work Step by Step
a) The formula for the frequency in a open pipe is: $f=\frac{nv}{2L}$ The question specifies fundamental frequency so n=1 (i.e. the first harmonic).
$Length = \frac{nv}{2f}$
$Length = \frac{1\times344 m/s}{2\times524 Hz}$
$$Length = 0.328 m$$
b) In a closed pipe, the formula for the frequency is $f=\frac{nv}{4L}$.
Since $f=\frac{v}{λ}$, we can rearrange for the wavelength and substitute the equation for the frequency to get: $ λ = \frac{4L}{n}$
Therefore, $$λ = \frac{4\times\times\times0.328 m}{1} = 1.312 m$$
c) $f=\frac{nv}{4L}$.
$$ f = \frac{1\times344 m/s}{4\times0.328 m} = 262.2 Hz$$
