Question

Ultrasound reflected from an oncoming bloodstream that is moving at 30.0 cm/s is mixed with the original frequency of 2.50 MHz to produce beats. What is the beat frequency?

a) 35 Hz
b) 40 Hz
c) 45 Hz
d) 50 Hz

Answer 1

The beat frequency can be calculated using the formula: beat frequency = |v - vo| / λ. Given the velocity of the bloodstream, the velocity of sound, and the ultrasound frequency, we can find the wavelength and then use it to calculate the beat frequency. The correct answer is not provided in the given options.

Step-by-step explanation:

The beat frequency can be found using the formula:

beat frequency = |v - vo| / λ

Where v is the velocity of the bloodstream, vo is the velocity of sound, and λ is the wavelength of the ultrasound.

First, we need to find the wavelength using the formula:

λ = v / f

Where f is the frequency of the ultrasound.

Substituting the given values:

λ = (30.0 cm/s) / (2.50 MHz)

Converting cm/s to m/s:

λ = (0.30 m/s) / (2.50 × 10^6 Hz)

Calculating λ:

λ = 1.2 × 10^-7 m

Now plug the values of λ and vo = 331 m/s into the formula:

beat frequency = |30.0 - 331| / (1.2 × 10^-7)

Calculating the beat frequency:

beat frequency = 301 / (1.2 × 10^-7)

beat frequency = 2.51 × 10^9 Hz

The beat frequency is approximately 2.51 GHz. Hence, the correct answer is not provided in the options given.