Solution: From the given question, we shall find the vector quantity among the
(A) Time , (B) Velocity, (C) Distance , (D) Speed
Concept: <u>Vector Quantity: </u>All those physical quantities which have magnitude as well as specific directions, are called Vector Quantities.
Here, Time, Distance and Speed have only magnitude but have no directions so they will be scalar quantities.
Now, <u>Velocity:</u> It is defined as the change in displacement per unit time. Since the change in the displacement will be in particular direction only. Hence, velocity will be the vector quantity.
Hence, the option (B) Velocity will be the correct option.
A steel piano wire, of length 1.150 m and mass of 4.80 g is stretched under a tension of 580.0 N.the speed of transverse waves on the wire would be 372.77 m/s
<h3>What is a sound wave?</h3>
It is a particular variety of mechanical waves made up of the disruption brought on by the movements of the energy. In an elastic medium like the air, a sound wave travels through compression and rarefaction.
For calculating the wave velocity of the sound waves generated from the piano can be calculated by the formula
V= √F/μ
where v is the wave velocity of the wave travel on the string
F is the tension in the string of piano
μ is the mass per unit length of the string
As given in question a steel piano wire, of length 1.150 m and mass of 4.80 g is stretched under a tension of 580.0 N.
The μ is the mass per unit length of the string would be
μ = 4.80/(1.150×1000)
μ = 0.0041739 kg/m
By substituting the respective values of the tension on the string and the density(mass per unit length) in the above formula of the wave velocity
V= √F/μ
V=√(580/0.0041739)
V = 372.77 m/s
Thus, the speed of transverse waves on the wire comes out to be 372.77 m/s
Learn more about sound waves from here
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Hi there!
We can begin by solving for the linear acceleration as we are given sufficient values to do so.
We can use the following equation:
vf = vi + at
Plug in given values:
4 = 9.7 + 4.4a
Solve for a:
a = -1.295 m/s²
We can use the following equation to convert from linear to angular acceleration:
a = αr
a/r = α
Thus:
-1.295/0.61 = -2.124 rad/sec² ⇒ 2.124 rad/sec² since counterclockwise is positive.
Now, we can find the angular displacement using the following:
θ = ωit + 1/2αt²
We must convert the initial velocity of the tire (9.7 m/s) to angular velocity:
v = ωr
v/r = ω
9.7/0.61 = 15.9 rad/sec
Plug into the equation:
θ = 15.9(4.4) + 1/2(2.124)(4.4²) = 20.56 rad
Answer:
W = 0.135 N
Explanation:
Given:
- y (x, t) = 8.50*cos(172*x -2730*t)
- Weight of string m*g = 0.0126 N
- Attached weight = W
Find:
The attached weight W given that Tension and W are equal.
Solution:
The general form of standing mechanical waves is given by:
y (x, t) = A*cos(k*x -w*t)
Where k = stiffness and w = angular frequency
Hence,
k = 172 and w = 2730
- Calculate wave speed V:
V = w / k = 2730 / 172 = 13.78 m/s
- Tension in the string T:
T = Y*V^2
where Y: is the mass per unit length of the string.
- The tension T and weight attached W are equal:
T = W = Y*V^2 = (w/L*g)*V^2
W = (0.0126 / 1.8*9.81)*(13.78)^2
W = 0.135 N
