The velocity of longitudinal waves in quartz crystal is 5.5 x106m/s.Thickness of quartz crystal is 0.05m. the frequency of thefirst mode of Vibration is ___________.D 1 9.3 x 10^3 Hz 110 x 10^3 Hz 0.02 Hz 5.5 x 10^7 Hz
Question
The velocity of longitudinal waves in quartz crystal is 5.5 x106m/s.Thickness of quartz crystal is 0.05m. the frequency of thefirst mode of Vibration is ___________.D 1 9.3 x 10^3 Hz 110 x 10^3 Hz 0.02 Hz 5.5 x 10^7 Hz
Solution
The frequency of the first mode of vibration can be calculated using the formula for the frequency of a wave, which is:
Frequency (f) = Velocity (v) / Wavelength (λ)
In this case, the wavelength is twice the thickness of the quartz crystal because the first mode of vibration involves the wave traveling to the top of the crystal and back down.
So, Wavelength (λ) = 2 * Thickness of the crystal = 2 * 0.05m = 0.1m
Now, we can substitute the values into the formula:
Frequency (f) = 5.5 x 10^6 m/s / 0.1m = 55 x 10^6 Hz
Therefore, the frequency of the first mode of vibration is 55 x 10^6 Hz. However, this option is not given in the choices. There might be a mistake in the question or the given options.
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