Question

PART ONE

Answer 1

Answer:

(a) 58 cm

(b) 591.4 Hz

(c) 246.5 cm

Explanation:

(a)

For closed organ pipe, the wavelength is given by

$\lambda=\frac {4L}{2n-1}$ where $\lambda$ is wavelength, L is the length of the pipe and n is the resonance

Substituting 217.5 m for L and 8 for n then the wavelength of the sound will be

$\lambda=\frac {4\times 217.5}{(2\times 8)-1}=58 cm$

(b)

We know that the speed of sound, v is a product of frequency and wavelength.

$v=\lambda f$

Making frequency the subject of the formula then

$f=\frac {v}{\lambda}$ and since the velocity is given as 343 m/s and wavelength is already found in part a above but now we change units from cm to m then

$f=\frac {343}{0.58}=591.3793103\\\boxed {\approx 591.4 Hz }$

(c)

We know that

$\lambda=\frac {4L}{2n-1}$

The next resonance will be the 9th and we know the wavelength hence making L the subject then

$L=\frac {\lambda \times (2n-1)}{4}\\\frac {58\times (2*9-1)}{4}\\\=\boxed{ 246.5 cm}$