Question

A person measures her heart rate by counting the number of beats in 30 s. If 36 ± 2 beats are counted in 30.0 ± 0.4 s, what is the heart rate and its uncertainty in beats per minute?

Answer 1

For the heart rate :

n = number of heat beats = 36

t = time taken to measure = 30 s = 30/60 min = 0.5 min            (since 1 min = 60 sec)

R = heart rate

Heart rate is given as

$R = \frac{n }{t}$

inserting the values

$R = \frac{36 }{0.5}$

R = 72 min⁻¹

For uncertainty :

Δn = uncertainty in number of heat beats = ± 2

Δt = uncertainty in time taken = ± 0.4 s = ± 0.4/60 min = ± 0.0067 min            (since 1 min = 60 sec)

ΔR = uncertainty in heart rate

uncertainty in Heart rate is given as

$\frac{\Delta R}{R}=\pm \left ( \frac{\Delta n}{n} + \frac{\Delta t}{t}\right )$

inserting the values

$\frac{\Delta R}{72}=\pm \left ( \frac{2}{36} + \frac{0.0067}{0.5}\right )$

ΔR = ± 4.96 min⁻¹