A Beating Heart — phryzby

Q. On an average, a human heart is found to beat 75 times in 1 min. What is its frequency, in hertz? expects 1.25 Hz

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Q. On an average, a human heart is found to beat 75 $N = 75$ times in 1 min $Δ t = 1$ min. What is its frequency, in hertz?

The playground

Inputs

beats

N

time

Δ t

1 min

Outputs

frequency

ν

The solution

Solved with PeriodicMotion

Given

$N = 75$
$Δ t = 1$ min

Find $ν$ .

Working

$Δ t = 1$ min $= 60$ s
frequency is repetitions a second(beating) $ν = \frac{N}{Δ t}$
$ν = \frac{75}{60}$
$ν = 1.25$ Hz
$ν \approx 1.25$ Hzto 3 significant figures

Conclusion

Frequency counts the beats in each second, so the beats in a minute are shared out over its sixty seconds.

The Ruby

1require_relative "../physics"23question :a_beating_heart do4  kind :numerical5  describes "On an average, a human heart is found to beat %{beats} times in %{time}. %{frequency}, in hertz?"6  given beats: "75"7  given time: "1 min"8  asks frequency: "What is its frequency"9end

1require_relative "../questions/a_beating_heart"2require_relative "../science/oscillations/periodic_motion"34solve :a_beating_heart, using: PeriodicMotion do5  objects :heart6  heart.goes(:beating)78  take beats: heart.repetitions9  take time: beating.time_taken1011  frequency = heart.frequency12  answer frequency:, in: "Hz", figures: 31314  conclusion "Frequency counts the beats in each second, so the beats in a minute are shared out over " \15             "its sixty seconds."16end

1require_relative "../solutions/a_beating_heart"23play_with :a_beating_heart do4  title "A Beating Heart"5end

The laws

quantity	written	units	within	from
position	$x$	m	—	Velocity
displacement	$Δ x$	m	—	Velocity
path length	$d$	m	—	Velocity
time taken	$Δ t$	s	0 … 1e+05	Velocity
average velocity	$v_{av}$	m/s	—	Velocity
average speed	$c_{av}$	m/s	—	Velocity
starting position	$x_{0}$	m	—	Velocity
final position	$x$	m	—	Velocity
repetitions	$N$	—	—	PeriodicMotion
frequency	$ν$	Hz	0 … ∞	PeriodicMotion
period	$T$	s	—	PeriodicMotion
displacement of heart during beating	$Δ x$	m	—
position of heart at end of beating	$x_{1}$	m	—
position of heart at start of beating	$x_{0}$	m	—
average velocity of heart during beating	$v_{av}$	m/s	—
time taken of beating	$Δ t$	s	0 … 1e+05
average speed of heart during beating	$c_{av}$	m/s	—
path length of heart during beating	$d$	m	—
frequency of heart	$ν$	Hz	0 … ∞
repetitions of heart during beating	$N$	—	—
period of ground	$T_{g}$	s	—
frequency of ground	$ν_{g}$	Hz	0 … ∞
period of heart	$T$	s	—

x_{0} \equiv x_{i} (start of motion)

starting position

x \equiv x_{i} (end of motion)

final position

d_{i} (whole) = d_{i} (part 1) + d_{i} (part 2)

path in parts

Δ t_{w} = Δ t_{p} + Δ t_{p}

time in parts

T_{b} = \frac{1}{ν_{b}}

period is the time of one

Δ x = x_{1} - x_{0}

change of position(beating)

v_{av} = \frac{Δ x}{Δ t}

displacement a time(beating)

c_{av} = \frac{d}{Δ t}

path a time(beating)

ν = \frac{N}{Δ t}

frequency is repetitions a second(beating)

T_{g} = \frac{1}{ν_{g}}

period is the time of one(ground)

T = \frac{1}{ν}

period is the time of one(heart)