Answer:
540m/s
Explanation:
Given parameters:
Frequency of the wave = 18000Hz
Wavelength of the wave = 0.03m
Unknown:
How fast is the wave traveling = ?
Solution:
How fast the wave is traveling is a measure of the speed of the wave;
Speed of wave = frequency x wavelength
Now insert the given parameters and solve;
Speed of wave = 18000 x 0.03 = 540m/s
Our primary method for localizing sound in the horizontal plane is to compare the arrival time of sound at each ear.
Let's call a the acceleration of the system. The problem says that the block m3 is static, so the acceleration is zero: a=0.
Calling
the tension of the string between m1 and m3, and
the tension of the string between m2 and m3, the problem can be solved by writing the following system of equations:
However, we know that a=0 and the problem asks only for
, so we just need to solve the first equation:
and so
Answer:
T₁= 75.25 N : Wire tension forming angle of 52° with horizontal
T₂ = 60.49 N : Wire tension forming angle of 40° with horizontal
Explanation:
We apply Newton's first law to the holiday decoration in equilibrium
Forces acting on holiday decoration:
T₁ : Wire tension forming angle of 52° with horizontal
T₂ : Wire tension forming angle of 40° with horizontal
W= m*g= 10 kg*9.8 m/s² = 98 N : weight of the decoration
∑Fx=0
T₁x -T₂x = 0
T₁x = T₂x
T₁*cos52° = T₂*cos40°
T₁= T₂*(cos40°) / (cos52°)
T₁= 1.244T₂ Equation (1)
∑Fy=0
T₁y+T₂y -W = 0
T₁*sin52° + T₂*sin40° - 98 = 0 Equation (2)
We replace T₁ of the equation (1) in the equation (2)
1.244T₂*sin52° + T₂*sin40° - 98 = 0
0.98T₂ + 0.643T₂ = 98
1.62T₂ = 98
T₂ = 98 / 1.62
T₂ = 60.49 N
We replace T₂ = 60.49 N in the Equation (1)
T₁= 1.244*60.49 N
T₁= 75.25 N
