(a) Audible wavelengths. The range of audible frequencies is...

(a) Audible wavelengths. The range of audible frequencies is from about $20 \mathrm{~Hz}$ to $20,000 \mathrm{~Hz}$. What is the range of the wavelengths of audible sound in air? (b) Visible light. The range of visible light extends from $380 \mathrm{nm}$ to $750 \mathrm{nm}$. What is the range of visible frequencies of light? (c) Brain surgery. Surgeons can remove brain tumors by using a cavitron ultrasonic surgical aspirator, which produces sound waves of frequency $23 \mathrm{kHz}$. What is the wavelength of these waves in air? (d) Sound in the body. What would be the wavelength of the sound in part (c) in bodily fluids in which the speed of sound is $1480 \mathrm{~m} / \mathrm{s}$ but the frequency is unchanged?

Key Concepts

Unit Conversion

Accurate analysis of wave phenomena often requires converting between units, such as from nanometers to meters or kilohertz to hertz. Consistent use of units is crucial to correctly apply physical formulas and obtain accurate results.

Electromagnetic Spectrum

This refers to the range of all types of electromagnetic radiation. Visible light is just a portion of this spectrum, and its properties are determined using the invariant speed of light. The relationship between wavelength and frequency within the spectrum is a key tool in understanding optical phenomena.

Medium-Dependent Wave Speed

The propagation speed of waves such as sound depends on the medium through which they travel. Different media (like air, water, or bodily fluids) have different speeds, which directly affects the wavelength for a given frequency.

Frequency-Wavelength Inverse Relationship

Because the wave speed is a constant in a given medium, frequency and wavelength are inversely proportional. An increase in frequency implies a decrease in wavelength and vice versa, a concept essential to understanding both sound and electromagnetic waves.

Wave Equation

This principle states that the speed of a wave (v) is the product of its frequency (f) and wavelength (?), expressed as v = f × ?. It is a fundamental relation used to connect the propagation speed of any wave to its other characteristics.

Transcript

00:01 Okay, so here we're dealing with audible wavelengths.

00:04 It says the range of audible frequencies, the frequencies you can hear, is about 20 hertz to 20 ,000 hertz.

00:13 It's a pretty large range, if you ask me.

00:17 And we want to know what the range of wavelengths is of audible sound and air.

00:26 So range of lambda.

00:30 So we can just here go ahead and use our handy reliance.

00:36 V is equal to lambda f, which holds for pretty much all traveling waves that we're going to deal with.

00:45 And go ahead and plug in the speed of sound in air here.

00:51 V is equal to 344 meters per second.

00:57 So for f is equal to 20 ,000 hertz, lambda is going to be v over f, which is equal to 344.

01:11 Meters per second over 20 ,000 hertz.

01:19 Remember, hertz is just one divided by second, which is about 1 .7 centimeters.

01:30 So that's a, that means the distance, the wavelength of a sound wave here in air, at the highest frequency you hear, is 1 .7 centimeters.

01:45 So you can visualize that kind of, between your hands.

01:49 It's kind of cool.

01:51 So for f is equal to 20 hertz, we get lambda is equal to the over f, which is 344 meters per second by 20 hertz is equal to 1.

02:11 Oh, actually 9 .1 .17 meters, which means that the wavelength for the lowest sound that you can hear is huge.

02:22 That's 17 meters.

02:23 That is a sizable amount.

02:26 That's over 45 feet, you know? so, yeah, it just shows that the range of human hearing corresponds to a very large range of void lengths.

02:39 And that's all for that problem.

02:43 That's all for part a, rather.

02:45 So we can go to part b now and discuss.

02:51 So now we're moving on to visible light.

02:53 It says the range of visible light from 300.

02:57 80 nanometers, so just right here, visible light.

03:03 So all the light you can see ranges from lambda is equal to 380 nanometers to, let's tidy this up a little bit, 750 nanometers.

03:26 And we want to know what the range of frequencies is.

03:33 So we use our same old v as equal to lambda f formula to get that, except here now, v is equal to the speed of light, which we reserve a special letter for c.

03:51 And that's approximately 3 times 10 to the 8 meters per second.

03:56 Very, very fast...

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