Respuesta :
Answer:
a) [tex]\lambda = \frac{3x10^8 m/s}{101300000 Hz}= 2.962 m[/tex]
b) [tex] f= \frac{343 m/s}{2.962 m}= 115.8 Hz[/tex]
Explanation:
For this case we have the following frequency given:
[tex] f= 101.3 MHz[/tex]
We can convert this into Hz like this:
[tex] f= 101.3 MHz * \frac{10^6 Hz}{1 MHz}= 101300000 Hz[/tex]
If we have a fundamental wave we need to satisfy the following condition:
[tex] v = \lambda f[/tex]
If we solve for the wavelength we got:
[tex] \lambda = \frac{v}{f}[/tex]
We know that the velocity of the light is [tex] v= 3x10^8 m/s[/tex]
And if we replace into the last formula we got:
[tex]\lambda = \frac{3x10^8 m/s}{101300000 Hz}= 2.962 m[/tex]
Part b
For this case we can use the same formula but on this case the velocity of the sound at 20C is approximately 343 m/s, the frequency is given by:
[tex] f = \frac{v}{\lambda}[/tex]
We use the same wavelenght from the previous part [tex] \lamba = 2.962 m[/tex]
And if we replace the new values we got:
[tex] f= \frac{343 m/s}{2.962 m}= 115.8 Hz[/tex]
A. The wavelength is the wave is 2.96 m
B. The frequency of the wave is 115.87 Hz
The velocity, frequency and wavelength of a wave are related according to the following equation:
velocity (v) = wavelength (λ) x frequency (f)
v = λf
- With the above formula, we can obtain the answers to the questions are follow:
A. Determination of the wavelength
Frequency (f) = 101.3 MHz = 101.3×10⁶ Hz.
Velocity (v) = 3×10⁸ m/s
Wavelength (λ) =?
[tex]\lambda = \frac{v}{f} \\ \\ \lambda = \frac{3 \times {10}^{8} }{101.3 \times {10}^{6}} \\ \\ \lambda = 2.96 \: m[/tex]
Therefore, the wavelength of wave is 2.96 m
B. Determination of the frequency of the wave
Velocity (v) of sound in air = 343 m/s
Wavelength (λ) = 2.96 m
Frequency (f) =?
[tex]f = \frac{v}{\lambda} \\ \\ f = \frac{343}{2.96} \\ \\ f = 115.87 \: Hz[/tex]
Therefore, the frequency of the sound wave is 115.87 Hz
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