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1. Deaf musicians detect sounds by sensing vibrations which travel through the floor. Somepeople say that these musicians keep in time better than others, because sound travels fasterthrough a wooden floor than through the air.

Calculate the speed of sound in wood.

Young modulus of wood =1 !"a

Density of wood = ## kg m$%

Speed of sound = &&&&&&&&&&&&&&&&&&&&&&& '()

*or musicians 1# m apart, is there a noticeable time difference between sounds which travel

through the wooden floor and through the air+ ustify your answer with relevant calculations.

Speed of sound in air = %%#ms$1

'()-he amplitude of the sound vibrations which arrive through the floor is three times larger thanthat through the air. ow do the intensities of these sounds compare+

'()

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State how the amplitude of echoes is reduced in a concert hail.

'1)

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(. -he speaker shown below is used to produce the bass notes in a music system.

-he cone moves with simple harmonic motion and it emits a single$fre0uency sound of 1## .2hen it is producing a loud sound, the cone moves through a ma3imum distance of (.# mm.

-he e0uation that mathematically describes the displacement of the cone is x = 1.# 3 1#$% cos (4 t .

Show that the data for this speaker lead to the numbers in the e0uation above.

'()Calculate

'i) the ma3imum acceleration of the cone

5a3imum acceleration = &&&&&&&&&&&&&&&&&&&& 

'ii) the ma3imum speed of the cone

5a3imum speed = &&&&&&&&&&&&&&&&&&&& '%)

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6n the grid below sketch the acceleration$time graph for two cycles of vibration of this speakercone used under these conditions. 7dd suitable numerical scales to the two a3es.

'%)83plain why designers ensure that bass speakers have a natural fre0uency of oscillation muchgreater than 1## .

'()

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%. 9n 1::; the comet Shoemaker$<evy approached the planet upiter on a collision course. ustbefore the collision, the comet consisted of at least 1/ separate fragments as shown in thepicture.

 7ll the fragments had originally been combined in a single comet with a diameter of : km.Comets like this are made of ice with trapped dust and gas and have a typical density of##kgm$%.

Show that the minimum mass for the original comet which formed Shoemaker$<evy was about( 3 1#1; kg.

'%) 7s a single comet, Shoemaker$<evy had previously approached upiter in 1::(. 7t its closest,the near side of the comet was : ### km from the centre of upiter. 7t this near side of thecomet, upiter>s gravitational field strength was 1%./;4 ?kg$1.

Calculate upiter>s gravitational field strength at the far side of the comet.

'5ass of upiter = 1.4:4/ 3 1#(/ kg.!, gravitational constant=./(# 3 1#$11 ?m( kg$().

'%)

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83plain why the comet broke apart as it passed upiter in 1::(.

'()State one difference and one similarity between gravitational fields and electric fields.

Difference

Similarity

'()

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;. 7 scientist was investigating the effects of e3treme pressure, as might be e3perienced deep inthe ocean. e used a polystyrene cup in his investigation and a total pressure of %. 3 1#/ "awas applied to it, s0uashing the cup.

-he volume of the air in the cup>s polystyrene bubbles was originally / 3 1#$ m%.Calculate the new volume in the bubbles in the s0uashed cup.

 7ssume that the temperature remains constant. 7tmospheric pressure = 1.# 3 1# "a.

@olume = &&&&&&&&&&&&&&&&& '%)

State one other assumption made in the calculation above.

'1)

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9n reality, the temperature drops when going down into the ocean from ( AC at the surface to1# AC at the depth modelled in the e3periment. Calculate the percentage change in the averagekinetic energy of the air molecules as a result of this temperature change.

'%)

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. Scientists have worked out the age of the 5oon by dating the rocks brought back by the 7pollomissions. -hey use the decay of potassium$;# to stable argon$;# in the rocksB this process has

a half life of 1.% 3 1#: years. 9n one rock sample, the scientists found #.4; µg of argon$;# and

#.1# µg of potassium$;#.

se the data above to calculate the age of the 5oon.

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