To detect tumours in soft tissues, ultrasonic waves with a frequency of 4.5 MHz are utilized. The speed of sound is 1.5 km s^ -1 in tissue and 340 m s^ -1 in air. Determine the wavelength of these ultrasonic waves in

Correct answer: B. 7.6 × 10^ -5 m , 3.3 × 10^ -4 m Given frequency, f = 4.5 MHz = 4.5 × 10^ 6 Hz Speed of sound in air, v_ a = 340 m s^ -1 Speed of sound in tissue, v_ t = 1.5 km s^ -1 = 1500 m s^ -1 The wavelength of the ultrasonic waves in air is given by: λ_ a = v_ a f = 340 4.5 × 10^ 6 m λ_ a 75.5 × 10^ -6 m 7.6 × 10^ -5 m The wavelength of the ultrasonic waves in tissue is given by: λ_ t = v_ t f = 1500 4.5 × 10^ 6 m λ_ t 333.3 × 10^ -6 m 3.3 × 10^ -4 m Thus, the wavelengths in air and tissue are 7.6 × 10^ -5 m and 3.3 × 10^ -4 m respectively.

Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Sound Waves

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Sound Waves

To detect tumours in soft tissues, ultrasonic waves with a...

To detect tumours in soft tissues, ultrasonic waves with a frequency of

4.5 \text{ MHz}

are utilized. The speed of sound is

1.5 \text{ km s}^{-1}

in tissue and

340 \text{ m s}^{-1}

in air. Determine the wavelength of these ultrasonic waves in air and in tissue, respectively.

Options

A $3.3 \times 10^{-4} \text{ m}$ , $7.6 \times 10^{-5} \text{ m}$
B $7.6 \times 10^{-5} \text{ m}$ , $3.3 \times 10^{-4} \text{ m}$
C $7.6 \times 10^{-4} \text{ m}$ , $3.3 \times 10^{-5} \text{ m}$
D $1.5 \times 10^{-3} \text{ m}$ , $3.4 \times 10^{-4} \text{ m}$

Correct answer

B. $7.6 \times 10^{-5} \text{ m}$ , $3.3 \times 10^{-4} \text{ m}$

Step-by-step solution

Given frequency,

f = 4.5 \text{ MHz} = 4.5 \times 10^{6} \text{ Hz}

Speed of sound in air,

v_{a} = 340 \text{ m s}^{-1}

Speed of sound in tissue,

v_{t} = 1.5 \text{ km s}^{-1} = 1500 \text{ m s}^{-1}

The wavelength of the ultrasonic waves in air is given by:

\lambda_{a} = \dfrac{v_{a}}{f} = \dfrac{340}{4.5 \times 10^{6}} \text{ m}

\lambda_{a} \approx 75.5 \times 10^{-6} \text{ m} \approx 7.6 \times 10^{-5} \text{ m}

The wavelength of the ultrasonic waves in tissue is given by:

\lambda_{t} = \dfrac{v_{t}}{f} = \dfrac{1500}{4.5 \times 10^{6}} \text{ m}

\lambda_{t} \approx 333.3 \times 10^{-6} \text{ m} \approx 3.3 \times 10^{-4} \text{ m}

Thus, the wavelengths in air and tissue are

7.6 \times 10^{-5} \text{ m}

and

3.3 \times 10^{-4} \text{ m}

respectively.

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