15.7 A hospital uses an ultrasonic scanner to locate tumours in a tissue. What is the wavelength of sound in the tissue in which the speed of sound is 1.7 km s–1 ? The operating frequency of the scanner is 4.2 MHz.
Operating frequency of the scanner, = 4.2 MHz = 4.2 Hz
The wavelength of sound in the tissue is given as:
= = 4.05 m
<p>Speed of sound in tissue, v = 1.7 km/s = 1.7 <span title="Click to copy mathml"><math><mo>×</mo><mi></mi><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msup></math></span> m/s</p><p>Operating frequency of the scanner, <span title="Click to copy mathml"><math><mi>ν</mi></math></span> = 4.2 MHz = 4.2 <span title="Click to copy mathml"><math><mo>×</mo><mi></mi><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>6</mn></mrow></mrow></msup></math></span> Hz</p><p>The wavelength of sound in the tissue is given as:</p><p><span title="Click to copy mathml"><math><mi>λ</mi><mo>=</mo><mi></mi><mfrac><mrow><mrow><mi>v</mi></mrow></mrow><mrow><mrow><mi>ν</mi></mrow></mrow></mfrac></math></span> = <span title="Click to copy mathml"><math><mfrac><mrow><mrow><mn>1.7</mn><mi mathvariant="normal"></mi><mo>×</mo><mi></mi><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>3</mn></mrow></mrow></msup></mrow></mrow><mrow><mrow><mn>4.2</mn><mi mathvariant="normal"></mi><mo>×</mo><mi></mi><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mn>6</mn></mrow></mrow></msup></mrow></mrow></mfrac></math></span> = 4.05 <span title="Click to copy mathml"><math><mo>×</mo><msup><mrow><mrow><mn>10</mn></mrow></mrow><mrow><mrow><mo>-</mo><mn>4</mn></mrow></mrow></msup></math></span> m</p>
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