What is the wavelength of ultrasonic energy in lead at 1 MHz with a velocity of 2.1 × 10^5 cm/s?

What is the wavelength of ultrasonic energy in lead at 1 MHz with a velocity of 2.1 × 10^5 cm/s?

• A. 0.21 cm
• B. 21 cm
• C. 0.48 cm
• D. 4.8 × 10^5 cm

Answer: (A)

To calculate the wavelength of ultrasonic energy, you can use the relationship between velocity, frequency, and wavelength, which is expressed by the formula: \[ \text{Wavelength} (\lambda) = \frac{\text{Velocity} (v)}{\text{Frequency} (f)} \] In this case, the frequency is given as 1 MHz, which is equal to \( 1 \times 10^6 \) Hz, and the velocity is \( 2.1 \times 10^5 \) cm/s. Plugging these values into the equation: \[ \lambda = \frac{2.1 \times 10^5 \text{ cm/s}}{1 \times 10^6 \text{ Hz}} = 0.21 \text{ cm} \] This calculation shows that the wavelength of ultrasonic energy in lead at the specified frequency is indeed 0.21 cm, making this the correct answer. Understanding the relationship between these concepts is crucial for students working with ultrasonic testing methods, as the wavelength can significantly affect the resolution and detection capabilities of the equipment being used.

To calculate the wavelength of ultrasonic energy, you can use the relationship between velocity, frequency, and wavelength, which is expressed by the formula:

[ \text{Wavelength} (\lambda) = \frac{\text{Velocity} (v)}{\text{Frequency} (f)} ]

In this case, the frequency is given as 1 MHz, which is equal to ( 1 \times 10^6 ) Hz, and the velocity is ( 2.1 \times 10^5 ) cm/s.

Plugging these values into the equation:

[ \lambda = \frac{2.1 \times 10^5 \text{ cm/s}}{1 \times 10^6 \text{ Hz}} = 0.21 \text{ cm} ]

This calculation shows that the wavelength of ultrasonic energy in lead at the specified frequency is indeed 0.21 cm, making this the correct answer.

Understanding the relationship between these concepts is crucial for students working with ultrasonic testing methods, as the wavelength can significantly affect the resolution and detection capabilities of the equipment being used.