Question

Diagnostic ultrasound of frequency 3.78 MHz is used to examine tumors in soft tissue. (a) What is the wavelength in air of such a sound wave? (b) If the speed of sound in tissue is 1560 m/s, what is the wavelength of this wave in tissue? (Take the speed of sound in air to be 343 m/s.)

Answer 1

`8.886* 10^(-5) m` m is the wavelength in air of such a sound wave.

`4.041* 10^(-4) m` is the wavelength of this wave in tissue.

Step-by-step explanation:

a)Frequency of the diagnostic ultrasound = 3.78 MHz =
`3.86* 10^6 Hz`

Wavelength of the diagnostic ultrasound =
`\lambda`

c = speed of sound in air

`\\u=(c)/(\lambda )`

`3.86* 10^6 s^(-1)=(343 m/s)/(\lambda )`

`\lambda =8.886* 10^(-5) m`

`8.886* 10^(-5) m` is the wavelength in air of such a sound wave.

b)If the speed of sound in tissue is 1560 m/s.

Wavelength of the diagnostic ultrasound =
`\lambda`

c = speed of sound in tissue = 1560 m/s

`\\u=(c)/(\lambda )`

`3.86* 10^6 s^(-1)=(1560 m/s)/(\lambda )`

`\lambda =4.041* 10^(-4) m`

`4.041* 10^(-4) m` is the wavelength of this wave in tissue.

Answer 2

The wavelength in air and in tissue are
`9.07*10^(-5)\ m` and
`4.13*10^(-4)\ m`.

Step-by-step explanation:

Given that,

Frequency = 3.78 MHz

We need to calculate the wavelength in air

Using formula of wavelength

`\lambda=(v)/(f)`

Where, v = speed of sound in air

f = frequency

Put the value into the formula

`\lambda=(343)/(3.78*10^(6))`

`\lambda=9.07*10^(-5)\ m`

We need to calculate the wavelength in tissue

Using formula of wavelength

`\lambda=(v)/(f)`

Where, v = speed of sound in tissue

f = frequency

Put the value into the formula

`\lambda=(1560)/(3.78*10^(6))`

`\lambda=4.13*10^(-4)\ m`

Hence, The wavelength in air and in tissue are
`9.07*10^(-5)\ m` and
`4.13*10^(-4)\ m`.