You generate a wave in a spring, stretched out on the floor, by oscillating your hand back and forth at a frequency of 1.6 Hz. The wave has a 1.5-m wavelength. If the wave takes 2.9 s to travel to the other end of the spring and back to your hand, what is the length of the stretched spring?
f=1.6 Hz
λ=1.5 m
v= λf=1.5•1.6=2.4 m/s
L=vt/2=2.4•2.9/2=3.48 m.
To find the length of the stretched spring, we can use the wave speed formula:
Wave speed (v) = Frequency (f) × Wavelength (λ)
In this case, the frequency of the wave is given as 1.6 Hz, and the wavelength is given as 1.5 m. So we can substitute these values into the formula:
v = 1.6 Hz × 1.5 m
Now we need to find the wave speed. The wave speed is equal to the distance travelled by the wave (2 times the length of the spring) divided by the time taken:
v = (2 × length of the spring) / time
We are given that the wave takes 2.9 s to travel to the other end of the spring and back to your hand. So we can plug in the values:
1.6 Hz × 1.5 m = (2 × length of the spring) / 2.9 s
Now we can rearrange this equation to solve for the length of the spring:
(1.6 Hz × 1.5 m) × (2.9 s) = 2 × length of the spring
Rearranging, we get:
Length of the spring = (1.6 Hz × 1.5 m × 2.9 s) / 2
Now we can calculate the length of the spring:
Length of the spring = (1.6 Hz × 1.5 m × 2.9 s) / 2 = 3.744 m
Therefore, the length of the stretched spring is approximately 3.744 meters.