Concepts Of Physics MCQ Edition [Volume 1]PhysicsSound Waves
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 air and in tissue, respectively.
Options
- A3.3 10⁻⁴ m , 7.6 10⁻⁵ m
- B7.6 10⁻⁵ m , 3.3 10⁻⁴ m
- C7.6 10⁻⁴ m , 3.3 10⁻⁵ m
- D1.5 10⁻³ m , 3.4 10⁻⁴ m
Correct answer
B. 7.6 10⁻⁵ m , 3.3 10⁻⁴ m
Step-by-step solution
Given frequency, f = 4.5 MHz = 4.5 10⁶ 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: _ a = v_ a f = 340 4.5 10⁶ m _ a 75.5 10⁻⁶ m 7.6 10⁻⁵ m The wavelength of the ultrasonic waves in tissue is given by: _ t = v_ t f = 1500 4.5 10⁶ m _ 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.