Question
A hospital uses an ultrasonic scanner to locate tumours in a tissue. The operating frequency of the scanner is $$4.2\,MHz.$$ The speed of sound in a tissue is $$1.7\,km/s.$$ The wavelength of sound in tissue is close to
A.
$$4 \times {10^{ - 4}}m$$
B.
$$8 \times {10^{ - 4}}m$$
C.
$$4 \times {10^{ - 3}}m$$
D.
$$8 \times {10^{ - 3}}m$$
Answer :
$$4 \times {10^{ - 4}}m$$
Solution :
$$\eqalign{
& {\text{Frequency}}\,\,\left( n \right) = 4.2\,MHz = 4.2 \times {10^6}\,Hz\,\,{\text{and}} \cr
& {\text{speed}}\,{\text{of sound}}\,\left( v \right) = 1.7\,km/s = 1.7 \times {10^3}\,m/s. \cr} $$
Wave length of sound in tissue
$$\left( \lambda \right) = \frac{v}{n} = \frac{{1.7 \times {{10}^3}}}{{4.2 \times {{10}^6}}} = 4 \times {10^{ - 4}}m.$$