1) c. 2 m/s
Explanation:
The relationship between frequency, wavelength and speed of a wave is
where
v is the speed
is the wavelength
f is the frequency
For the wave in this problem,
f = 4 Hz
So, the speed is
2) a. 2.8 m/s
The speed of the wave on a string is given
where
T is the tension in the string
is the linear mass density
In this problem, we have:
(final tension in the rope, which is twice the initial tension)
--> mass density of the rope
Substituting into the formula, we find
Answer:
29.75 revolutions
Explanation:
The kinematic formula for distance, given a uniform acceleration a and an initial velocity v₀, is
This car is starting from rest, so v₀ = 0 m/s. Additionally, we have a = 9.2/9.7 m/s² and t = 9.7 s. Plugging these values into our equation:
So, the car has travelled 44.62 m in 9.7 seconds - we want to know how many of the tire's <em>circumferences</em> fit into that distance, so we'll first have to calculate that circumference. The formula for the circumference of a circle given its diameter is , which in this case is 47.8π cm, or, using π ≈ 3.14, 47.8(3.14) = 150.092 cm.
Before we divide the distance travelled by the circumference, we need to make sure we're using the same units. 1 m = 100 cm, so 105.092 cm ≈ 1.5 m. Dividing 44.62 m by this value, we find the number of revs is
revolutions