Question

(a) Audible wavelengths. The range of audible frequencies is from about\(20 Hz to 20,000 Hz\) . What is the range of the wavelengths of audible sound in air? (b) Visible light. The range of visible light extends from\(380 nm to 750 nm\) . 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\(23 kHz\). 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 {m \mathord{\left/

{\vphantom {m s}} \right.

\\s}\)but the frequency is unchanged?

Short answer

(a) \(1.7\,cm\,\,to\,\,17\,m\)

Step-by-step solution

Given Data

Range of frequency \(20 Hz to 20,000 Hz\)

Concept/ Formula used

For humans, the audible frequency range is around 20 Hz to 20,000 Hz (20 kHz). It's customary to divide this range into at least three categories for descriptive purposes: lows, mids, and highs.

Formula:

\(\lambda = \frac{v}{f}\)

Where, \(v\) is velocity and \(f\)is frequency of sound

Calculation for wavelength  

(a)

\(v = 344\,{m \mathord{\left/

{\vphantom {m s}} \right.

\\s}\)

For \(f = 20,000\,Hz\)

\(\begin{aligned}{c}\lambda = \frac{v}{f}\\ = \frac{{344\,{m \mathord{\left/

{\vphantom {m s}} \right.

\\s}}}{{20,000\,Hz}}\\ = 1.7\,cm\end{aligned}\)

For \(f = 20\,Hz\)

\(\begin{aligned}{c}\lambda = \frac{v}{f}\\ = \frac{{344\,{m \mathord{\left/

{\vphantom {m s}} \right.

\\s}}}{{20Hz}}\\ = 17\,m\end{aligned}\)

The range of wavelengths is\(1.7\,cm\,\,to\,\,17\,m\)