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Question
Ultrasonic waves of frequency 4.5 MHz are used to detect tumour in soft tissue. The speed of sound in tissue is 1.5 km s−1 and that in air is 340 m s−1. Find the wavelength of this ultrasonic wave in air and in tissue.
Solution
(a) Given:
Frequency of ultrasonic wave f = 4.5 MHz = 4.5 × 106 Hz
Velocity of air v = 340 m/s
Speed of sound in tissue = 1.5 km/s
Wavelength λ = ?
As we know, \[v = f\lambda\]
\[\therefore \lambda = \frac{340}{4 . 5 \times {10}^6}\]
\[ \Rightarrow \lambda = 7 . 6 \times {10}^{- 5} m\]
(b) Velocity of sound in tissue vtissue= 1500 m/s
\[\lambda = \frac{v_{tissue}}{f}\]
\[ \Rightarrow \lambda = \frac{1500}{4 . 5 \times {10}^{- 6}} \text{ m }\]
\[ \Rightarrow \lambda = 3 . 3 \times {10}^{- 4} \text{ m }\]
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