Question

What is the wavelength of ultrasound in water?
A) 1.5mm
B) 3mm
C) 4.5mm
D) 6.0mm

Answer 1

Hint:Wavelength of the wave is given by:
$\lambda ={\displaystyle \frac{v}{f}}$ ,wavelength of the wave is given by $\lambda$ ,v is the velocity and f is the frequency .

Here, in the question velocity of ultrasound is not given but generally we assume the value of velocity as 1540m/s ,which is also the speed of ultrasound in tissues of the human body.
Using the above relation we will find out the wavelength of the ultrasound.

Complete step by step solution:
Let’s define ultrasound and wavelength first:

Ultrasound: ultrasound are sound waves which have a higher audible limit than human hearing limit .Ultrasound waves are similar to normal sound waves except they are not audible to human ears. Hearing limit of human ears is 20hz to 20khz , ultrasound waves are above this range. Range of ultrasound waves is generally 1 to 10Mhz .

Wavelength is the distance between identical points in the adjacent cycles of a waveform.
Now, let’s calculate the wavelength of the ultrasound, using the formula we have mentioned in the hint .
$\lambda ={\displaystyle \frac{v}{f}}$( let's take the lowest frequency range 1Mhz and speed of sound as 1540m/s)
$\Rightarrow \lambda ={\displaystyle \frac{1540}{1\times {10}^6}}$(substituting the numerical values)
  $$\begin{gathered} \Rightarrow \lambda =1540\times {10}^{-6} \\ \Rightarrow \lambda =1.54\times {10}^{-3} \\ \Rightarrow \lambda =1.54mm \end{gathered}$$ (1m=10-3mm)

Thus, option 1 is correct.

Note: Ultrasound waves are generally used in the medical field for examining the problematic areas of the internal organs of the human body like the intestines, liver, kidney ,gallbladder ,and heart. Ultrasound waves are also used by submarines to detect underwater objects and ships of enemies .