An earthquake wave has a wave length of 523m and travels with a speed of 4.6km through a portiin of Earths crust.
a) what is its frequency?
b) if it travels into a different portion of Earths crust, where its speed is 7.5km/s,what is its new wavelength?
L = 523 m.
V = 4.6 km/s. = 4600 m/s.
a. L = V*(1/F) = V/F = 523 m
4600/F = 523
523F = 4600
F = 8.8 c/s = 8.8 Hz.
b. L = V/F = 7500/8.8 = 852.3 m.
To answer these questions, we will need to use the formula for wave speed:
Wave speed (v) = frequency (f) x wavelength (λ).
a) To find the frequency of the earthquake wave, we can rearrange the formula:
frequency (f) = wave speed (v) / wavelength (λ).
Given that the wave speed is 4.6 km/s and the wavelength is 523 m, we need to convert the wave speed to meters per second:
4.6 km/s = 4.6 x 1000 m/1 s = 4600 m/s.
Now we can substitute the values into the formula:
frequency (f) = 4600 m/s / 523 m.
Calculating this division gives us:
frequency (f) = 8.796 Hz (rounded to three decimal places).
Therefore, the frequency of the earthquake wave is approximately 8.796 Hz.
b) To find the new wavelength when the wave travels through a different portion of Earth's crust with a wave speed of 7.5 km/s, we can use a similar approach:
wave speed (v) = frequency (f) x wavelength (λ).
Given that the wave speed is 7.5 km/s, we convert it to meters per second:
7.5 km/s = 7.5 x 1000 m/1 s = 7500 m/s.
We can rearrange the formula to solve for the new wavelength:
wavelength (λ) = wave speed (v) / frequency (f).
Remember that we need to calculate the frequency first and then substitute it into the formula.
Using the previous frequency we found (8.796 Hz), we can calculate the new wavelength:
wavelength (λ) = 7500 m/s / 8.796 Hz.
Calculating this division gives us:
wavelength (λ) = 853.313 m (rounded to three decimal places).
Therefore, when the earthquake wave travels through a different portion of Earth's crust with a wave speed of 7.5 km/s, the new wavelength is approximately 853.313 m.