You are listening to the radio when one of your favorite songs comes on, so you turn up the volume. If you managed to increase t
1 answer:
To solve this problem we need to apply the corresponding sound intensity measured from the logarithmic scale. Since in the range of intensities that the human ear can detect without pain there are large differences in the number of figures used on a linear scale, it is usual to use a logarithmic scale. The unit most used in the logarithmic scale is the decibel yes described as
Where,
I = Acoustic intensity in linear scale
= Hearing threshold
The value in decibels is 17dB, then
Using properties of logarithms we have,
Therefore the factor that the intensity of the sound was
You might be interested in
The position of an oscillating mass is given by:
where A is the amplitude of the oscillation, the angular frequency and t the time.
The velocity of the oscillating mass can be found by calculating the derivative of the position:
In this problem, A=2.0 cm and , so if we substitute these data and t=0.4 s we can find the velocity at t=0.4 s:
2) 20.2 m/s
In the first 4.4 seconds of its motion, the blue car accelerates at a rate of
So its final velocity after these 4.4 seconds is
where
u = 0 is the initial velocity (the car starts from rest)
a is the acceleration
t is the time
Substituting t = 4.4 s, we find
After this, the car continues at a constant speed for another 8.5 s, so it will keep this velocity until
Therefore, the velocity of the car 10.4 seconds after it starts will still be 20.2 m/s.
3) 216.2 m
The distance travelled by the car during the first 4.4 s of the motion is given by
where
u = 0 is the initial velocity
is the time
is the acceleration
Substituting,
The car then continues for another 8.5 s at a constant speed, so the distance travelled in the second part is
where
is the new velocity
is the time
Substituting,
So the total distance travelled before the brakes are applied is
4)
We are told that the blue car comes to a spot at a distance of 247 meters from the start. Therefore, the distance travelled by the car while the brakes are applied is
We can find the acceleration of the car during this part by using the SUVAT equation:
where
is the final velocity (zero since the car comes to a stop)
is the velocity of the car at the moment the brakes are applied
a is the acceleration
Solving for a, we find