An element 'X' does not liberate hydrogen from acids but react with oxygen to give a black coloured product.Identify 'X' and the black coloured product and also write the reaction of 'X' with oxygen?
Answers
Answer:
When you pluck a guitar string, the resulting sound has a steady tone and lasts a long time ((Figure)). The string vibrates around an equilibrium position, and one oscillation is completed when the string starts from the initial position, travels to one of the extreme positions, then to the other extreme position, and returns to its initial position. We define periodic motion to be any motion that repeats itself at regular time intervals, such as exhibited by the guitar string or by a child swinging on a swing. In this section, we study the basic characteristics of oscillations and their mathematical description.
A photograph of a guitar being played.
Figure 15.2 When a guitar string is plucked, the string oscillates up and down in periodic motion. The vibrating string causes the surrounding air molecules to oscillate, producing sound waves. (credit: Yutaka Tsutano)
Period and Frequency in Oscillations
In the absence of friction, the time to complete one oscillation remains constant and is called the period (T). Its units are usually seconds, but may be any convenient unit of time. The word ‘period’ refers to the time for some event whether repetitive or not, but in this chapter, we shall deal primarily in periodic motion, which is by definition repetitive.
A concept closely related to period is the frequency of an event. Frequency (f) is defined to be the number of events per unit time. For periodic motion, frequency is the number of oscillations per unit time. The relationship between frequency and period is
f
=
1
T
.
The SI unit for frequency is the hertz (Hz) and is defined as one cycle per second:
1
Hz
=
1
cycle
sec
or
1
Hz
=
1
s
=
1
s
−
1
.
A cycle is one complete oscillation.
Explanation:
EXAMPLE
Determining the Frequency of Medical Ultrasound
Ultrasound machines are used by medical professionals to make images for examining internal organs of the body. An ultrasound machine emits high-frequency sound waves, which reflect off the organs, and a computer receives the waves, using them to create a picture. We can use the formulas presented in this module to determine the frequency, based on what we know about oscillations. Consider a medical imaging device that produces ultrasound by oscillating with a period of
0.400
μ
s
. What is the frequency of this oscillation?
Strategy
The period (T) is given and we are asked to find frequency (f).
Solution
Substitute
0.400
μ
s
for T in
f
=
1
T
:
f
=
1
T
=
1
0.400
×
10
−
6
s
.
Solve to find
f
=
2.50
×
10
6
Hz
.
Significance
This frequency of sound is much higher than the highest frequency that humans can hear (the range of human hearing is 20 Hz to 20,000 Hz); therefore, it is called ultrasound. Appropriate oscillations at this frequency generate ultrasound used for noninvasive medical diagnoses, such as observations of a fetus in the womb.
Characteristics of Simple Harmonic Motion
A very common type of periodic motion is called simple harmonic motion (SHM). A system that oscillates with SHM is called a simple harmonic oscillator.
Simple Harmonic Motion
In simple harmonic motion, the acceleration of the system, and therefore the net force, is proportional to the displacement and acts in the opposite direction of the displacement.
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Explanation: