Question 224: EM waves

Question

The magnetic field in a electromagnetic wave is given by
$$B_y=2 	imes 10^{-7} \sin \left(0.5+10^3 x+1.5 	imes 10^{11} tight) \mathrm{T}$$
The frequency of the wave is (in GHz)

Accepted Answer

We start with the given magnetic field in the electromagnetic wave:
$$ B_y = 2 	imes 10^{-7} \sin\left(0.5 + 10^3 x + 1.5 	imes 10^{11} tight) \quad 	ext{T} $$
In a wave equation, the phase typically has the form
$$ 	ext{phase} = kx - \omega t + \phi_0, $$
where:
$$k$$ is the wave number,
$$\omega$$ is the angular frequency, and
$$\phi_0$$ is a phase constant.
In our given expression, even though the signs may differ (a plus sign in front of the time term), the coefficient of $$t$$ still represents the angular frequency. Thus, we identify
$$ \omega = 1.5 	imes 10^{11}\ 	ext{rad/s}. $$
The relationship between the angular frequency and the frequency $$f$$ is given by:
$$ f = \frac{\omega}{2\pi}. $$
Substitute the value of $$\omega$$:
$$ f = \frac{1.5 	imes 10^{11}}{2\pi}. $$
Performing the calculation:
First, compute the denominator:
$$    2\pi \approx 6.2832.    $$
Now, divide:
$$    f \approx \frac{1.5 	imes 10^{11}}{6.2832} \approx 2.39 	imes 10^{10}\ 	ext{Hz}.    $$
Since 1 GHz equals $$10^9$$ Hz, we convert the frequency to GHz:
$$ f \approx \frac{2.39 	imes 10^{10}\ 	ext{Hz}}{10^9} = 23.9\ 	ext{GHz}. $$
Thus, the frequency of the wave is 23.9 GHz, which corresponds to Option D.

Answer

1.26 GHz

Answer

2.39 GHz

Answer

12.6 GHz

Answer

23.9 GHz

EM waves

The magnetic field in a electromagnetic wave is given by $B_y=2 \times 10^{-7} \sin \left(0.5+10^3 x+1.5 \times 10^{11} t\right) \mathrm{T}$ The frequency of the wave is (in GHz)

Choose the correct answer: