The velocity of a wave can be calculated by multiplying its frequency (f) by its wavelength (λ). Therefore, to find the wave's frequency, we can rearrange this equation to solve for f:
v = f * λ
Given the values:
Velocity (v) = 200 m/s Wavelength (λ) = 0.25 m
Substituting these values into the equation:
200 m/s = f * 0.25 m
To find the frequency (f), we divide both sides of the equation by 0.25 m:
f = 200 m/s / 0.25 m
f = 800 Hz
Therefore, the wave's frequency is 800 Hz.
If the wavelength in the same rope is changed to 0.5 m, we can calculate the resulting wave's speed and frequency using the same formula:
New Wavelength (λ) = 0.5 m
To find the new wave's speed, we rearrange the equation:
v = f * λ
Given: Velocity (v) = 200 m/s Wavelength (λ) = 0.5 m
Substituting the values:
200 m/s = f * 0.5 m
To find the frequency (f), we divide both sides of the equation by 0.5 m:
f = 200 m/s / 0.5 m
f = 400 Hz
Therefore, the resulting wave's frequency is 400 Hz.
To calculate the resulting wave's speed, we can use the original equation:
v = f * λ
Substituting the values:
Velocity (v) = ? Frequency (f) = 400 Hz Wavelength (λ) = 0.5 m
Rearranging the equation to solve for v:
v = f * λ v = 400 Hz * 0.5 m
v = 200 m/s
Therefore, the resulting wave's speed is 200 m/s.