A Pipe Closed at One End

Q. A pipe 20 cm long is closed at one end. The speed of sound in air is 340 m/s. Which harmonic mode of the pipe is resonantly excited by a 430 Hz source? expects 1

What the draft establishes

Fills in once a draft is checked.

The web of concepts

given read from the words equation asked

The equations it used

None yet.

Check an answer

Q. A pipe 20 cm $L = 20$ cm long is closed at one end. The speed of sound in air is 340 m/s $v = 340$ m/s. Which harmonic mode of the pipe is resonantly excited by a 430 Hz $ν = 430$ Hz source?

The playground

Inputs

length

L

20 cm

speed

v

340.0 m/s

source

ν

430 Hz

Outputs

harmonic

n

The solution

Solved with ClosedPipe

Given

$L = 20$ cm
$v = 340$ m/s
$ν = 430$ Hz

Find $n$ .

Working

$L = 20$ cm $= 0.2$ m
harmonics of a pipe closed at one end(pipe) $ν = \frac{n \cdot v}{4 \cdot L}$
$430 = \frac{n \cdot 340}{4 \cdot 0.2}$
$n = 1.01176471$
$n \approx 1$ to 1 significant figure

Conclusion

A pipe closed at one end sounds only odd multiples of its fundamental, the speed over four times its length; the source matches that fundamental.

The Ruby

1require_relative "../physics"23question :a_pipe_closed_at_one_end do4  kind :numerical5  describes "A pipe %{length} long is closed at one end. The speed of sound in air is %{speed}. %{harmonic} a " \6            "%{source} source?"7  given length: "20 cm"8  given speed: "340 m/s"9  given source: "430 Hz"10  asks harmonic: "Which harmonic mode of the pipe is resonantly excited by"11end

1require_relative "../questions/a_pipe_closed_at_one_end"2require_relative "../science/waves/closed_pipe"34solve :a_pipe_closed_at_one_end, using: ClosedPipe do5  objects :pipe67  take length: pipe.length_of_the_pipe8  take speed: v9  take source: pipe.frequency1011  harmonic = pipe.harmonic12  answer harmonic:, figures: 11314  conclusion "A pipe closed at one end sounds only odd multiples of its fundamental, the speed over four times " \15             "its length; the source matches that fundamental."16end

1require_relative "../solutions/a_pipe_closed_at_one_end"23play_with :a_pipe_closed_at_one_end do4  title "A Pipe Closed at One End"5end

The laws

quantity	written	units	within	from
speed of sound	$v$	m/s	—	ClosedPipe
length of the pipe	$L$	m	—	ClosedPipe
harmonic	$n$	—	—	ClosedPipe
frequency	$ν$	Hz	0 … ∞	ClosedPipe
frequency of ground	$ν_{g}$	Hz	0 … ∞
harmonic of ground	$n_{g}$	—	—
length of the pipe of ground	$L_{g}$	m	—
frequency of pipe	$ν$	Hz	0 … ∞
harmonic of pipe	$n$	—	—
length of the pipe of pipe	$L$	m	—

ν_{p} = \frac{n_{p} \cdot v}{4 \cdot L_{p}}

harmonics of a pipe closed at one end

ν_{g} = \frac{n_{g} \cdot v}{4 \cdot L_{g}}

harmonics of a pipe closed at one end(ground)

ν = \frac{n \cdot v}{4 \cdot L}

harmonics of a pipe closed at one end(pipe)