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Sound

Question
ICSEENIPH10005538

i) Draw a graph between displacement and the time for a body executing free vibrations.

ii) Where can a body execute free vibrations?

Solution

i) For a body executing free vibrations, the graph between displacement and the time is as shown below:
WiredFaculty
ii) The oscillations of  a body, when set into vibrations by any external force, and then left to itself, executes free vibrations.
For example, a tuning fork when stuck with a hammer starts vibrating and it continues to vibrate for a while.  

Question
ICSEENIPH10005539

i) State the safe limit of sound level in terms of decibel for human hearing.

ii) Name the characteristics of sound in relation to its waveform.  

Solution

i) The sound level 30 dB to 10 dB has the soothing sensation.

ii) Quality (or timbre)                                                                            

Question
ICSEENIPH10005540

A person standing between two vertical cliffs and 480 m from the nearest cliff shouts. He hears the first echo after 3 s and the second echo 2 s later.

Calculate:

i) The speed of sound.

ii) The distance of the other cliff from the person.

Solution

i) Total distance travelled by the sound in going and coming back = 2 x 480 m.
Speed of sound =fraction numerator left parenthesis Total space distance space travelled right parenthesis over denominator left parenthesis Time space taken right parenthesis end fraction equals space space fraction numerator left parenthesis 2 space cross times 480 right parenthesis over denominator 3 end fraction equals 320 space straight m divided by straight s space
Time taken to reach second echo = 3+ 2 = 5 sec
Therefore, v =  fraction numerator 2 straight d over denominator straight t end fraction
⟹ d equals space fraction numerator v t over denominator 2 end fraction 
ii) Distance of other cliff from the person = fraction numerator 320 space cross times 5 over denominator 2 end fraction equals 800 space m

Question
ICSEENIPH10005541

In the diagram alongside, A, B, C, D are four pendulums suspended from the same elastic string PQ. The length of A and C are equal to each other while the length of the pendulum B is smaller than that of D. Pendulum A is set into a mode of vibrations.

i) Name the type of vibrations taking place in pendulum B and D?

ii) What is the state of the pendulum C?

iii) State the reason for the type of vibrations in pendulum B and C. 

Solution

i) B and D would be in a state of forced vibration.

ii) Since the length of the pendulum, C is same as that of A, therefore, it is in the state of resonance.

iii) The pendulum C has its length same as that of A, therefore, its natural time period is also same that of a and both remain in the same phase so resonance takes place. But, B’s length is lesser than the length of A, hence B would vibrate with smaller amplitude.