Question

1. What is the wavelength of a 2.0 MHz ultrasound wave traveling through aluminum?
2. What frequency of electromagnetic wave would have the same wavelength as the ultrasound wave of part a?

Short answer

The wavelength of a 2.0 MHz ultrasound wave traveling through aluminum is$3.21\times {10}^{-3}m$ .

The frequency of electromagnetic wave would have the same wavelength as the ultrasound wave is $9.35\times {10}^{10}Hz$.

Step-by-step solution

Given information:

The frequency of the ultrasound wave is $f=2\times {10}^{6}Hz$

Velocity of the wave travelling through Aluminium is v_aluminium=6420 m/s

Calculating the wavelength:

Wavelength is defined as the distance between consecutive crests or troughs in a wave.

The formula to calculate the wavelength in terms of the velocity of the wave through the medium is given by $\lambda =\frac{v_{aluminium}}{f}$

Substitute 2 MHz for f into the above formula to calculate the wavelength.

$$\begin{gathered} \lambda =\frac{6420m/s}{2\times {10}^{6}Hz} \\ =3.21\times {10}^{-3}m \end{gathered}$$

Therefore, the wavelength of a 2.0 MHz ultrasound wave traveling through aluminum is$3.21\times {10}^{-3}m$.

Calculating the frequency of the electromagnetic wave:

The electromagnetic waves travels at speed of light in vacuum=c= $3\times {10}^{8}m/s$

Substituting in the above formula to calculate the frequency.

$f=\frac{c}{\lambda }$

Substitute $3.21\times {10}^{-3}m$for $\lambda$and $3\times {10}^{8}m/s$for c into the above formula to calculate f.

$$\begin{gathered} f=\frac{3\times {10}^{8}m/s}{3.21\times {10}^{-3}m} \\ =9.35\times {10}^{10}Hz \end{gathered}$$

Therefore, the frequency of electromagnetic wave would have the same wavelength as the ultrasound wave is$9.35\times {10}^{10}Hz$.