Introduction: The Nature of Science and Physics

A piano tuner hears a beat every 2.00 s when listening to a 264.0 Hz tuning fork and a single piano string. What are the two possible frequencies of the string?

A ball is thrown straight up. It passes a 2.00 m high window 7.50 m off the ground on its path up and takes 1.30s to go past the window. What was the ball’s initial velocity?

What are the closest frequencies to \[500\;{\rm{Hz}}\]that an average person can clearly distinguish as being different in frequency from \[500\;{\rm{Hz}}\]? The sounds are not present simultaneously.

Diffraction spreading for a flashlight is insignificant compared with other limitations in its optics, such as spherical aberrations in its mirror. To show this, calculate the minimum angular spreading of a flashlight beam that is originally \(5.00\,{\rm{cm}}\) in diameter with an average wavelength of \(600\,{\rm{nm}}\).

If your radio is producing an average sound intensity level of \({\rm{85}}\;{\rm{dB}}\), what is the next lowest sound intensity level that is clearly less intense??

Using approximate values, calculate the slope of the curve in Figure 2.62 to verify that the velocity at t= 30 sec is 0.238 m/s. Assume all values are known to 3 significant figures 

Three adjacent keys on a piano (F, F-sharp, and G) are struck simultaneously, producing frequencies of 349, 370 and 392 Hz. What beat frequencies are produced by this discordant combination?

Integrated Concepts

How much time is needed for a surgical cauterize to raise the temperature of \(1.00{\rm{ }}\;g\) of tissue from \(37.0^\circ C\) to \(100^\circ C\) and then boil away \(0.500{\rm{ }}g\) of water, if it puts out \(2.00\;{\rm{ }}mA\) at \(15.0{\rm{ }}kV\)? Ignore heat transfer to the surroundings.

(a) An excimer laser used for vision correction emits 193 - nm UV. Calculate the photon energy in eV.

(b) These photons are used to evaporate corneal tissue, which is very similar to water in its properties. Calculate the amount of energy needed per molecule of water to make the phase change from liquid to gas. That is, divide the heat of vaporization in kJ/kg by the number of water molecules in a kilogram.

(c) Convert this to eV and compare to the photon energy. Discuss the implications.

A very large, superconducting solenoid such as one used in MRI scans, stores \(1.00{\rm{ }}MJ\) of energy in its magnetic field when \(100{\rm{ }}A\) flows. (a) Find its self-inductance. (b) If the coils “go normal,” they gain resistance and start to dissipate thermal energy. What temperature increase is produced if all the stored energy goes into heating the \(1000{\rm{ }}kg\) magnet, given its average specific heat is ?

One way to force air into an unconscious person’s lungs is to squeeze on a balloon appropriately connected to the subject. What force must you exert on the balloon with your hands to create a gauge pressure of \[{\rm{4}}{\rm{.00 cm}}\] water, assuming you squeeze on an effective area of \[{\rm{50 c}}{{\rm{m}}^{\rm{2}}}\]?

Heroes in movies hide beneath water and breathe through a hollow reed (villains never catch on to this trick). In practice, you cannot inhale in this manner if your lungs are more than \[{\rm{60}}{\rm{.0 cm}}\] below the surface. What is the maximum negative gauge pressure you can create in your lungs on dry land, assuming you can achieve −\[{\rm{3}}{\rm{.00 cm}}\] water pressure with your lungs \[{\rm{60}}{\rm{.0 cm}}\] below the surface?

What is the ratio of intensities of two sounds of identical frequency if the first is just barely discernible as louder to a person than the second?

What is the sound intensity level in decibels of ultrasound of intensity \[{10^5}{\rm{ W}} \cdot {{\rm{m}}^{ - 2}}\], used to pulverize tissue during surgery?

Find the sound intensity level in decibels of \[{\rm{2 \times 1}}{{\rm{0}}^{{\rm{ - 2}}}}{\rm{ W}} \cdot {{\rm{m}}^{{\rm{ - 2}}}}\] ultrasound used in medical diagnostics.

The time delay between transmission and the arrival of the reflected

wave of a signal using ultrasound traveling through a piece of fat tissue was 0.13ms. At what depth did this reflection occur?

During heavy lifting, a disk between spinal vertebrae is subjected to a \({\rm{5000 N}}\) compressional force. (a) What pressure is created, assuming that the disk has a uniform circular cross-section \({\rm{2}}{\rm{.00 cm}}\) in radius? (b) What deformation is produced if the disk is \({\rm{0}}{\rm{.800 cm}}\) thick and has Young’s modulus of \({\rm{1}}{\rm{.5 \times 1}}{{\rm{0}}^{\rm{9}}}{\rm{ N/}}{{\rm{m}}^{\rm{2}}}\)?.

(a) Find the size of the smallest detail observable in human tissue with 20MHz ultrasound. (b) Is its effective penetration depth great enough to examine the entire eye (about 3.00cm is needed)? (c) What is the wavelength of such ultrasound in air \[{0^o}{\rm{C }}\]?

(a) Echo times are measured by diagnostic ultrasound scanners to determine distances to reflecting surfaces in a patient. What is the difference in echo times for tissues that are 3.50 and 3.60cm beneath the surface? (This difference is the minimum resolving time for the scanner to see details as small as 0.100cm, or 1.00mm. Discrimination of smaller time differences is needed to see smaller details.) (b) Discuss whether the period T of this ultrasound must be smaller than the minimum time resolution. If so, what is the minimum frequency of the ultrasound, and is that out of the normal range for a diagnostic ultrasound?

(a) How far apart are two layers of tissue that produce echoes having round-trip times (used to measure distances) that differ by \[{\rm{0}}{\rm{.750 \mu s}}\]? (b) What minimum frequency must the ultrasound have to see the detail of this small?

A short circuit in a\(120{\rm{ }}V\) appliance cord has a \(0.500{\rm{ }}\Omega \) resistance. Calculate the temperature rise of the \(2.00{\rm{ }}g\) of surrounding materials, assuming their specific heat capacity is  and that it takes \(0.0500{\rm{ }}s\) for a circuit breaker to interrupt the current. Is this likely to be damaging?

Models are particularly useful in relativity and quantum mechanics, where conditions are outside those normally encountered by humans. What is a model?

If two different theories describe experimental observations equally well, can one be said to be more valid than the other (assuming both use accepted rules of logic)?

What determines the validity of a theory?

Certain criteria must be satisfied if a measurement or observation is to be believed. Will the criteria necessarily be as strict for an expected result as for an unexpected result?

Can the validity of a model be limited, or must it be universally valid? How does this compare to the required validity of a theory or a law?

Classical physics is a good approximation to modern physics under certain circumstances. What are they?

When is it necessary to use relativistic quantum mechanics?

Can classical physics be used to accurately describe a satellite moving at a speed of $\mathbf{7500}\mathbf{ }\mathit{m}\mathbf{/}\mathit{s}$? Explain why or why not.

Identify some advantages of metric units.

The speed limit on some interstate highways is roughly  100 km/h . (a) What is this in meters per second? (b) How many miles per hour is this?

Show that 1.0 m/s = 3.6 km/h. Hint: Show the explicit steps involved in converting 1.0 m/s = 3.6 km/h

The speed of sound is measured to be \({\rm{342 }}{{\rm{m}} \mathord{\left/ {\vphantom {{\rm{m}} {\rm{s}}}} \right. \\} {\rm{s}}}\) on a certain day. What is this in km/h?

A can contains 375 mL of soda. How much is left after 308 mL is removed?

If a marathon runner averages\({\bf{9}}.{\bf{5}}{\rm{ }}{{{\rm{mi}}} \mathord{\left/ {\vphantom {{{\rm{mi}}} {\rm{h}}}} \right. \\} {\rm{h}}}\), how long does it take him or her to run a \(26.22{\rm{ mi}}\) marathon?

The sides of a small rectangular box are measured to be \({\bf{1}}.{\bf{80}} \pm {\bf{0}}.{\bf{01}}{\rm{ }}{\bf{cm}}\), \({\bf{2}}.{\bf{05}} \pm {\bf{0}}.{\bf{02}}{\rm{ }}{\bf{cm}}\), and \({\bf{3}}.{\bf{1}} \pm {\bf{0}}.{\bf{1}}{\rm{ }}{\bf{cm}}\) long. Calculate its volume and uncertainty in cubic centimeters

When non-metric units were used in the United Kingdom, a unit of mass called the pound-mass \(\left( {{\bf{lbm}}} \right)\) was employed, where\({\bf{1}}{\rm{ }}{\bf{lbm}} = {\bf{0}}.{\bf{4539}}{\rm{ }}{\bf{kg}}\). (a) If there is an uncertainty of \({\bf{0}}.{\bf{0001}}{\rm{ }}{\bf{kg}}\) in the pound-mass unit, what is its percent uncertainty? (b) Based on that percent uncertainty, what mass in pound-mass has an uncertainty of \({\bf{1}}{\rm{ }}{\bf{kg}}\) when converted to kilograms?

The length and width of a rectangular room are measured to be \({\bf{3}}.{\bf{955}}{\rm{ }} \pm {\rm{ }}{\bf{0}}.{\bf{005m}}\) and \({\bf{3}}.{\bf{050}}{\rm{ }} \pm {\rm{ }}{\bf{0}}.{\bf{005m}}\). Calculate the area of the room and its uncertainty in square meters.

How many heartbeats are there in a lifetime?

Question: How many times longer than the mean life of an extremely unstable atomic nucleus is the lifetime of a human? (Hint: The lifetime of an unstable atomic nucleus is on the order of\({\bf{1}}{{\bf{0}}^{ - {\bf{22}}}}{\rm{ }}{\bf{s}}\).

Approximately how many atoms thick is a cell membrane, assuming all atoms there average about twice the size of a hydrogen atom?