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Chapter 13: Problem 16

A doctor counts 77 heartbeats in 1 minute. What are the corresponding period and frequency?

Short Answer

Expert verified
The heart's frequency is approximately 1.283 Hz, and the corresponding period is approximately 0.78 seconds.

Step by step solution

01

Identifying The Given Variables

From the problem, it is understood that the doctor counts 77 heartbeats in 1 minute. So, the frequency 'f' is 77 beats per minute.
02

Calculating The Frequency in Hz

Frequency is typically measured in Hertz (Hz). 1 Hz is equivalent to 1 event per second. Therefore, to convert the frequency to Hz, divide the number of beats by the number of seconds in a minute. Expressing frequency in Hz gives \( f = 77 \, beats/min \, \times \, (1 \, min / 60 \, sec) = 1.283 \, Hz \).
03

Calculating The Period

The period (T) is the reciprocal of the frequency. Therefore, to calculate the period, take the inverse of the frequency. This gives \( T = 1/f = 1/1.283 \, Hz = 0.78 \, sec \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Frequency in Hertz
The concept of frequency in Hertz (Hz) is foundational in understanding oscillatory and wave phenomena in physics. Hertz is the unit of frequency in the International System of Units (SI), named after the German physicist Heinrich Hertz. It quantifies how often an event occurs per unit of time, with one Hertz equivalent to one event per second.

When discussing heartbeat rates, measuring the frequency in Hertz provides a standardized way to convey how often the heart beats over time. Instead of stating the heartbeats per minute, conversion to Hertz allows for a uniform comparison to other periodic events, regardless of the time unit.
Period Calculation
The period of an event is the duration of time it takes for one cycle or occurrence of the event to complete. The period (T) is thus the reciprocal of the frequency (f). Mathematically, this relationship is expressed as:
\[ T = \frac{1}{f} \]
If the frequency of a heartbeat is 1.283 Hz, as in our problem, the period is the inverse of this number. Calculating the period allows us to understand the regularity of heartbeats. For instance, in medicine, period calculations might help in diagnosing irregular heart rhythms, also known as arrhythmias.
Heartbeat Rate
Heartbeat rate, usually referred to as heart rate, is a crucial measure of health and fitness. It is typically counted as the number of heartbeats per minute. A doctor counting 77 beats in one minute is finding the heart rate of a patient. Knowing this heartbeat rate can help in diagnosing cardiac conditions and can guide the treatment options. The rate at which the heart beats can vary with exercise, illness, injury, or emotional stress and typically ranges between 60 to 100 beats per minute for a resting adult.
Unit Conversion
Unit conversion is a vital skill in physics and other sciences, enabling us to convert measurements from one unit to another. Conversion is important for standardization of units when comparing different types of measurements. In our exercise, the heartbeat rate, initially measured in beats per minute, is converted to Hertz for frequency.

Here's how the conversion is done: To get Hertz from beats per minute, divide the number of beats by 60, as there are 60 seconds in a minute. This is expressed as:\[ f_{Hz} = \frac{\text{beats per minute}}{60} \]
Using the right conversions ensures clear communication in scientific disciplines and is essential when analyzing and comparing data.

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Most popular questions from this chapter

One pendulum consists of a solid rod of mass \(m\) and length \(L\) and another consists of a compact ball of the same mass \(m\) on the end of a massless string of the same length \(L\). Which has the greater period? Why?

Show that \(x(t)=a \cos \omega t-b \sin \omega t\) represents simple harmonic motion, as in Equation \(13.8,\) with \(A=\sqrt{a^{2}+b^{2}}\) and \(\phi=\tan ^{-1}(b / a)\)

A massless spring with \(k=74 \mathrm{N} / \mathrm{m}\) hangs from the ceiling. A \(490-\mathrm{g}\) mass is hooked onto the unstretched spring and allowed to drop. Find (a) the amplitude and (b) the period of the resulting

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