I'm not sure which units I should convert this to

[KittyCat1534]

Homework Statement:: Hello, I have a simple question which goes like this:

Medical ultrasound waves travel at about 1392.8 m/s in soft tissue. Higher frequencies provide clearer images but don't penetrate to deeper organs. Find the wavelengths (mm) of 1.7-MHz ultrasound used in fetal imaging.

My question is , what is wavelengths(mm) ? Are they referring to megameter or mili meter in cases such as this?
Relevant Equations:: Wavelength = Wave speed / Frequency

Wavelength = Wave speed / Frequency

Wavelength = 1392.8 / 1.7 = 819

 

[fresh_42]

Homework Statement:: Hello, I have a simple question which goes like this:

Medical ultrasound waves travel at about 1392.8 m/s in soft tissue. Higher frequencies provide clearer images but don't penetrate to deeper organs. Find the wavelengths (mm) of 1.7-MHz ultrasound used in fetal imaging.

My question is , what is wavelengths(mm) ? Are they referring to megameter or mili meter in cases such as this?
Relevant Equations:: Wavelength = Wave speed / Frequency

Wavelength = Wave speed / Frequency

Wavelength = 1392.8 / 1.7 = 819

Speed is measured in $[m/s]$ and frequency in $[1/s]$, so if you divide both you get $[m/s]:[1/s]=[m/s]\cdot [ s ]=[ m ]$. The resulting number is in meter. Wavelengths are short, so the meter result is usually transformed into $[ mm ]$ for millimeter (a thousandth of a meter), $[\mu m]$ for micrometer (a millionth of a meter), or $[ nm ]$ for nanometer (a billionth of a meter).

The shorter the wavelength the more the energy.
And always use the units in any calculation, always!

 

[kuruman]

My question is , what is wavelengths(mm) ? Are they referring to megameter or mili meter in cases such as this?

Lower case m is "milli" (10^-3).
Upper case M is "Mega" (10⁶).
Smaller letter goes with smaller unit and bigger letter with bigger unit.

A detailed list of SI prefixes can be found here. Note that prefix symbols are capitalized when greater than or equal to 10⁶ otherwise they are lower case.

I note that your calculation is meaningless because it lacks units. If your number "819" is supposed to be meters, then that's a wavelength of about half a mile, much larger than the size of an organ in a typical patient. You need to convert 1.7 MHz to Hz before doing the division.

 

[fresh_42]

You need to convert 1.7 MHz to Hz before doing the division.

And as just explained: the M stands for 'mega', i.e. one million times. Hertz is another word for $[1/s]$. So $1.7 \,MHz= 1,700,000 \,[1/s]\;=$ oscillating $1.7$ million times per second.

 

[KittyCat1534]

Speed is measured in $[m/s]$ and frequency in $[1/s]$, so if you divide both you get $[m/s]:[1/s]=[m/s]\cdot [ s ]=[ m ]$. The resulting number is in meter. Wavelengths are short, so the meter result is usually transformed into $[ mm ]$ for millimeter (a thousandth of a meter), $[\mu m]$ for micrometer (a millionth of a meter), or $[ nm ]$ for nanometer (a billionth of a meter).

The shorter the wavelength the more the energy.
And always use the units in any calculation, always!

Thanks!

 

[KittyCat1534]

Lower case m is "milli" (10^-3).
Upper case M is "Mega" (10⁶).
Smaller letter goes with smaller unit and bigger letter with bigger unit.

A detailed list of SI prefixes can be found here. Note that prefix symbols are capitalized when greater than or equal to 10⁶ otherwise they are lower case.

I note that your calculation is meaningless because it lacks units. If your number "819" is supposed to be meters, then that's a wavelength of about half a mile, much larger than the size of an organ in a typical patient. You need to convert 1.7 MHz to Hz before doing the division.

Oh I see, do you think I need to memorize all of the prefixes?

 

[jbriggs444]

Oh I see, do you think I need to memorize all of the prefixes?

For physics class, you can probably get by with memorizing the big four:

m - milli (1/1000) e.g. millimeters or milliliters.
c - centi (1/100) e.g. centimeters or cubic centimeters
k - kilo (1000) e.g. kilometers or kilograms
$\mu$ - micro (1/1,000,000) e.g. micron (micrometer) or microsecond

The d (deci) and h (hecta) prefixes are rarely used. The M (mega), G (giga) and T(tera) prefixes tend to get used mostly for high frequencies (Megahertz, Gigahertz, Terahertz) in my experience. The nano, pico, atto and femto prefixes tend not to appear in first year physics.

I can count on the fingers of one hand the number of times I've needed peta, exa, zetta and yotta. With four fingers left over. (I think I looked up exabyte once because it was a brand name).

Edit: Thanks, @sysprog for the corrections.

 

[sysprog]

For physics class, you can probably get by with memorizing the big four:

m - milli (1/1000) e.g. millimeters or milliliters.
c - centi (1/100) e.g. centimeters or cubic centimeters
k - kilo (1000) e.g. kilometers or kilograms
$\mu$ - micro (1/1,000,000) e.g. micron (micrometer) or microsecond

The d (deci) and h (hecta) prefixes are rarely used. The M (mega), G (giga) and T(tera) prefixes tend to get used mostly for high frequencies (Megahertz, Gigahertz, Terahertz) in my experience. The nano, pico, atto and femto prefixes tend not to appear in first year physics.

I can count on the fingers of one hand the number of times I've needed peta, exa, yetta and zotta. With four fingers left over. (I think I looked up exabyte once because it was a brand name).

It's zetta and yotta $-$ it seems like exa, then yotta, then zetta would be more alphabetic, but I guess that's not what 'they' were going for . . .

Exascale processing is just around the corner $-$

Exascale Computing Project - Los Alamos National Lab

What is exascale computing?

2:27
Exascale: The next frontier in computing

Exascale computing refers to computing systems capable of at least one exaflop or a billion billion [floating point] calculations per second (1018). That is 50 times faster than the most powerful supercomputers being used today and represents a thousand-fold increase over the first petascale computer that came into operation in 2008. How we use these large-scale simulation resources is the key to solving some of today’s most pressing problems, including clean energy production, nuclear reactor lifetime extension and nuclear stockpile aging.

 

[fresh_42]

Oh I see, do you think I need to memorize all of the prefixes?

No. It is convenient to know them for $10$ up to the $\pm 3,\pm 6, \pm 9$, but we live in times of links