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# General questions: Six questions to learn concepts

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1. The Moon is centripetally accelerating towards the Earth. Explain why it is not getting closer to the Earth.

2. Why is it easier to hold a 10lb weight next to your body instead of with your arm outstretched?

3. When you design a building in an earthquake region, how should the natural frequencies of oscillation of the building compare to the typical earthquake frequencies and why? Explain.

4. What is the purpose of frets on a guitar? In terms of frequency of the vibration of the strings; explain their use.

5. When you inhale helium and speak, your voice becomes far higher in pitch.

6. You hold a tuning fork in front of you in a stationary position. Another tuning work of the same frequency is moving toward you at a fair speed. Explain what you hear and why.

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## SOLUTION This solution is FREE courtesy of BrainMass!

1. The Moon is centripetally accelerating towards the Earth. Explain why it is not getting closer to the Earth
The acceleration of a body is the rate of change of its velocity. Thus if the velocity of a body changes with time, it is accelerating.
Now velocity is a vector quantity. A vector is represents the magnitude and direction both of the quantity. Such quantity will change by changing its magnitude, its direction or both.
When a body moves in a circular path with constant speed, the magnitude of its velocity remains constant while its direction continuously changes. Thus the velocity vector changes in direction. This corresponds to the acceleration of the body. This acceleration is always towards the center of the circular path and that is why called centripetal acceleration.
To produce acceleration, a force is required. The component of the force along the direction of motion changes magnitude of velocity while the component of force perpendicular to the direction of motion changes direction of motion only.
The moon moves in a circular path round the earth. The gravitational force experienced by the moon behaves as the centripetal force which produces centripetal acceleration which is changing the direction of motion just enough to keep it in a circular path with the distance between them as radius and hence the distance of the moon from the earth does not changes.

2. Why is it easier to hold a 10lb weight next to your body instead of with your arm outstretched?

A force can change the state of rest or of uniform linear motion of a body as well as it can change the state of rest or uniform rotational motion of a body. The rotational effect of the force is called a torque which is given by the product of the force and its perpendicular distance from axis of rotation. Thus if the force is nearer to the axis its rotational effect is less and increases with distance from the axis of rotation.
Now to keep a body in equilibrium, net force on it must be equal to zero as well as net torque on it should be zero.
To hold a weight we have to apply a force equal and opposite to it. So to lift a weight of 10 lb we have to apply a force of 10 lb in upward direction. If the weight is nearer to the body the torque due to the weight is less but as we outstretched the arm the weight is same but as its perpendicular distance from the shoulder joint is more its rotational effect i.e. the torque is increased and thus the tension at the shoulder joint and mussels experienced is more. Thus to hold the weight with outstretched arm is not that much easier.
3. When you design a building in an earthquake region, how should the natural frequencies of oscillation of the building compare to the typical earthquake frequencies and why? Explain
Everybody may have free oscillations with a particular frequency called its natural frequency and the oscillations are called free oscillations.
A body can made to vibrate by a periodic force of any frequency, after some irregular oscillations the body will start vibrating with the frequency of applied force and such oscillations are called forced oscillations.
When the frequency of the periodic force applied to the body is same as its natural frequency, the amplitude of oscillations of the body increases to a very large value and this is called resonance.
At the time of earthquake there should not be resonance between the periodic force of earthquake waves and the building and thus the building should be designed in such a way that its natural frequency will be much bellow or much higher than the common earthquake frequencies.
4. What is the purpose of frets on a guitar? In terms of frequency of the vibration of the strings, explain their use in 100 words or less
The characteristics of sound are its loudness, pitch and quality.
The pitch is the tone of the sound depends on its frequency. With different frequencies gives us different musical notes.
When a stretched string vibrates, its frequency varies with its vibrating length. Longer the string, lower the note.
With the string of guitar pushed against different frets, allowing different lengths of the sting to vibrate and thus produces different notes. While playing it these different notes are arranged to give a pattern of notes and this will make music.

5. When you inhale helium and speak, your voice becomes far higher in pitch. Explain why in 100 words or less
We produce sound by vibrating air in our vocal cord which can be considered like an organ pipe. The pitch of the sound produced depends on the velocity of sound in air and the length of the organ pipe (vocal cord here). The frequency of sound increases with decrease in the density of air.
Frequency velocity of sound in air /density of air
Now if we inhale helium, as its density is less than that of air, the velocity of sound in helium will be more and thus the frequency of vibration increases. Resulting in the increase in pitch of sound we produce.
6. You hold a tuning fork in front of you in a stationary position. Another tuning work of the same frequency is moving toward you at a fair speed. Explain what you hear and why
The stationary tuning fork will give out sound of the same frequency with which it vibrates and thus we get the sound of same frequency say f.
When a source moves towards listener the frequency of sound it produces in air is higher than that of its actual frequency of vibration. The phenomenon is called Doppler's effect. Thus the sound of the fork moving towards us will having a bit higher frequency than f.
When two waves of different frequencies are present in the medium, they create beats. Here the intensity of the resulting wave changes with time between maximum and minimum. The period of beat is the time interval between two consecutive maxima. Inverse of time period is the beat frequency which is equal to the difference of the frequency of the two sounds.
Thus we will hear periodic increase and decrease in intensity of sound i.e. beats.

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