Question

Question:BIO Ultrasound and Infrasound. (a) Whale communication. Blue whales apparently communicate with each other using sound of frequency 17 Hz, which can be heard nearly 1000 km away in the ocean. What is the wavelength of such a sound in seawater, where the speed of sound is 1531 m/s? (b) Dolphin clicks. One type of sound that dolphins emit is a sharp click of wavelength 1.5 cm in the ocean. What is the frequency of such clicks? (c) Dog whistles. One brand of dog whistles claims a frequency of 25 kHz for its product. What is the wavelength of this sound? (d) Bats. While bats emit a wide variety of sounds, one type emits pulses of sound having a frequency between 39 kHz and 78 kHz. What is the range of wavelengths of this sound? (e) Sonograms. Ultrasound is used to view the interior of the body, much as x rays are utilized. For sharp imagery, the wavelength of the sound should be around one-fourth (or less) the size of the objects to be viewed. Approximately what frequency of sound is needed to produce a clear image of a tumor that is 1.0 mm across if the speed of sound in the tissue is 1550 m/s?

Short answer

(a)The wavelength of the sound in seawater is $90.05\mathrm{m}$.

Step-by-step solution

Given data

The given data can be given listed below as,

• The frequency of the sound is,$f=17\mathrm{H}\mathrm{z}$.
• The distance at which the sound can be heard is,$d=1000\mathrm{k}\mathrm{m}=1000000\mathrm{m}=1\times {10}^6\mathrm{m}$.
• The speed of the sound in seawater is, $v=1531\mathrm{m}/\mathrm{s}$ .

Concept

The sound waves required a medium, such as solid (object), liquid (water), and gas(air), for them to travel from one position to another position. The wavelength of such waves is influenced by the medium and the frequency of the wave itself.

(a) Calculation of the wavelength of the sound in seawater

The wavelength of the sound can be calculated using the expression,

$\lambda =\frac{v}{f}$

Substitute the value in the above expression, and we get,

$\begin{array}{c}\lambda =\frac{1531\mathrm{m}/\mathrm{s}}{17\mathrm{H}\mathrm{z}}\\ =90.05\mathrm{m}\end{array}$

Thus, The wavelength of the sound in seawater is $90.05\mathrm{m}$.