Tweety Bird hops up and down at a frequency of 0.4 Hz on a power line at the midpoint between the poles, which are separated by 18 m. Assuming Tweety is exciting the fundamental standing wave, find the speed of transverse waves on the power line. (Hint: What is the wavelength for this standing wave?) need to know how to get m/s?
If the wavelength is λ, you know that 18m = λ/2.
Now, speed (m/s) = 36m*.4/s = 14.4m/s
To find the speed of transverse waves on the power line, we first need to determine the wavelength of the standing wave created by Tweety's hopping.
The frequency of the wave, given as 0.4 Hz, represents the number of complete oscillations or cycles per second. In other words, Tweety hops up and down 0.4 times per second.
The wavelength (λ) is the distance between two consecutive points that are in phase with each other, or the distance traveled by one complete cycle of the wave.
To find the wavelength, we can use the formula:
λ = v/f
Where:
λ = wavelength
v = speed of the wave
f = frequency of the wave
We know the frequency (f) is 0.4 Hz, and we need to find the speed of the wave (v).
Now, since Tweety is exciting the fundamental standing wave (the lowest possible frequency), the wavelength will be twice the distance between the poles (18 m).
Therefore, we have:
λ = 2 * 18
λ = 36 m
Now, we can substitute the values for λ and f into the formula to solve for v:
36 = v/0.4
To isolate v, we multiply both sides of the equation by 0.4:
0.4 * 36 = v
The product of 0.4 and 36 gives us:
v = 14.4 m/s
Hence, the speed of transverse waves on the power line is 14.4 m/s.