Chapter 1 - Simple Harmonic Waves and Motions Flashcards
Describe oscillation or vibration
The to and fro motion of a body about a mean point is known as oscillation (i.e, strumming of a guitar string). Its behavior is described using the following terminologies:
Vibration cycle, which is one complete round trip of a oscillating body from its mean position to the two extremes on either side, returning to its original afterwards.
Displacement (x), the position of a vibrating body at any given time. Measured in metres (m)
Amplitude (A or x0) is the maximum distance an oscillating body travels to an from its mean position. Measured in meters as well.
Time is the period of seconds taken by a vibrating body to complete a full cycle. Measured in Seconds.
Frequency (f) is the measure of cycles completed by an oscillating body in one second. Measured in Hertz or cps.
What is the relation between time and frequency in simple harmonic motions and oscillations?
They are reciprocals of each other. The greater the time, the less the frequency of complete cycles undertaken by an oscillating body and vice versa. Mathematically, T= 1/f
What is net force?
The restoring force of an object about its mean point is known at net force. This is also referred to as restoring force because it tends to restore of pushes a body back to a its stable equilibrium of stable point.
What is simple harmonic motion?
Simple harmonic motion is a special type of periodic motion an object experiences by means of a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position, and acts towards the equilibrium position.
Formula for the time period of a pendulum system?
T= 2pi square root (l/g)
Restoring force of a pendulum is given by
fres=-mg sin0
What is damping?
The gradual slowing down of an object that reduces the oscillations of vibrations of the object.
time period of a spring mass system
T= 2pi square root (m/k)
vibratory motion which is not shm
Bouncing a ball on the floor is an example of vibratory motion that is not simple harmonic motion (SHM). This is because the acceleration of the ball is directed downward, not towards an equilibrium position.
Derive the formula used to find the length of a second pendulum on the earth and the moon
T= 2pi square root (l/g)
Taking square root.
T^2 = 4pi^2 (l/g)
l= gt^2 / 4pi^2
A pendulum of length 2m is vibrating at a planet. It completes its vibration in time 5s. What is the value of g at this planet? (formula)
Time period= T= 2pi square root (l/g)
Squaring and arranging the equation for “g”, we get
T^2 = 4pi^2 (l/g)
g = 4pi^2 (l/T^2)
what is the time period of a mass spring system if the mass attached to a spring is 500 g and its spring constant is 20 Nm (formula)
formula of time period of a spring mass system
Time period= 2pi square root (m/k* constant)
If 10 waves are produced on a long stretched string of length one metre. What is the wavelength of the waves? What will be the frequency of the waves if the speed of waves is 12 ms. (formula)
In case of 10 waves, the string will vibrate in 20 loops, so n= 20.
Length= 1, Speed V= 12
We know that λ= 2l/n (part 1, wavelength)
Since v=fλ, frequency=v/λ (part 2, frequency)
In a ripple tank of length 1.6 m, waves cover this length in 2 seconds. IF distance between the two consecutive troughs is 20 cm, then find the number of waves, frequency of waves and their time period
length d = 1.6, time= 2, since d=vt,
v=d/t
Distance between two troughs=wavelengths
λ=2o cm= 20/100 = 0.2
now, v=fλ, so frequency f=v/λ
time period=T=1/f
Number of waves = frequency = number of waves passed/ time taken
Number of waves= frequency . time
calculate the frequency of red light of wavelength 700 nm in a vacuum
wavelength 700nm= 700 . 10^-7 = 7. 10^-7
Speed of light= v =3 . 10^8 ms^-1
v=fλ = f=v/λ
formula for wavelength
λ=2l/n
A simple pendulum has time period T in murree and different in karachi. How would you make them the same.
Time period is given by T^2 = 4pi^2 (l/g). This shows that the time period of a pendulum is inveersely proportional to the square root of g. T = 1/ square root g. At higher altitudes, g decreases therefpre time period is greater. To make it the same as the one in karachi, we increase the length of the simple pendulum or decrease g in a simulation.
what will happen to the frequency of waves in a ripple tank if time period of electrical vibrator is decrease? what will happen to its wave speed?
we know the relation v=fλ means that v is proportional to λ, so frequency is proportional to 1/λ.
We also know that time period is the reciprocal of frequency. t=1/f. This shows that if the time period of electrical vibrator is decreased, then frequency will increase.
And as v=fλ =1/t .λ =λ/t, time is inversely proportional to the speed of waves, so if time period of electrical vibrator is decreased, then the speed of the wave will increase.
Why do waves refract at the boundary of shallow water and deep water in a ripple tank experiment?
because the waves’ speed is influenced by the depth of water, so its velocity changes when it enters deep water from shallow water. This is essentially a change in wavelength.
Under what conditions is water refracted the most?
When the opening is made small but still comparable to the wavelength of the waves. This means that waves diffract the most when the size of the opening in an obstacle is. less than or equal to the wavelength of generated waves.
Some masses are attached to different strings, one vibrates faster. Why?
The frequency at which a mass vibrates depends on factors like its mass, the tension in the string, and the length and stiffness of the string. Heavier masses vibrate slower, while higher tension or shorter strings result in faster vibrations. The combination of these factors explains why some masses vibrate faster than others. For example, when a diving board is stiff, it vibrates faster, and the shorter its period.
A simple pendulum has time period T, what will happen to its time period is if its thread length is shortened to half?
Time period = T = 2pi square root (l/g), now if length becomes half, we put l=1/2, so we get;
T= 2pi square root l/2g
= 1/ square root 2, [ 2 pi square root l/2g]
putting this together, we get T’=1/square root 2 multiplied by T.
This means that the time period of the pendulum will decrease by a factor of 1/square root 2 . T
difference between damped and undamped oscillation
Damped oscillations
Occur when energy is dissipated from an oscillating system due to resistive
forces like friction or air resistance
The amplitude of damped oscillations decreases steadily over time
Damping continues until the oscillator comes to rest at the equilibrium position
Undamped oscillations
Occur when there is no energy loss in the system
The amplitude of undamped oscillations remains constant over time
In undamped oscillations, no resistive force acts on the vibrating object
Define wave
A disturbance that moves outward from a point of origin, transferring energy via vibration over large distances.
