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PHYSICS 101 Section 103
Lecturer. D.F.Measday
Second Mid-term
Monday, March 11, 2002 i) Do all questions, on both sides of the sheet; each section has equal marks. ii) Write answers in space provided; working MUST be shown; give units in answer.
iii) Calculators permitted; but NO notes,books etc.
Formulae: S.H.M. x= A cos(ωt + φ) v = - Aω sin(ωt + φ) P.E. = kx 2

2  k m
 g
L
y = A sin( kx 
 t
 
) v
  f

 k
 y
 t
  A
 cos( kx   t
/2
 
 2
 t
2 y
 a y
  
2 y v ( sound )


 p


R T
M v ( wire )

T

)



2
 f

2

T k

 decibels

10 log
10
I
I
0
2


P

1
2

2
A
2 v f '

with I
0
= 10
–12
W / m f
 
 v  v
O v
S


2 sin
  v v
S
Equal Temperament Scale: frequency x 12 2 per semi-tone. Velocity of sound= 340m/s
1.a) A block of mass 5.00 kg is held at the bottom of an unstretched bungee cord. When the block is dropped it falls 20 cm before stopping, and then bounces back. What is k, the spring constant for the cord ? b) How long does it take to reach the bottom for the first time ?
2. a) An aircraft is travelling at Mach 2 (i.e. twice the speed of sound ). What is the cone angle for the sonic boom ? b) If the aircraft is flying at a height of 3 000 m, how long does it take the boom to reach you, from the time the aircraft is directly overhead?
3.a) A bat is coming in to land at its roost which is on a wall. When it is 10 m away, what is the time difference between the squeak, and its return to the bat ? b) If the bat is travelling at 36 km/hr, and squeaks at 80,000 Hz, what is the frequency that the bat hears in the echo ?
4.a) A transverse wave on a string obeys the equation
y = 0.100 sin ( 0.250 π x + 12.0 π t ) in MKS units.
What is the propagation direction and velocity of this wave ? b) What is the maximum transverse velocity of the string ? c) Sketch the wave at t = 2.00 seconds, giving units on both axes.
5. A flute is effectively a uniform tube, open at both ends. a) Sketch the displacement curves for the first 4 resonances. b). When the flute is 65 cm long its fundamental note is at 246.3 Hz, and when it is 45 cm long the fundamental is at 351.1 Hz. Assume the effective length is Δ cm longer than the actual length, calculate Δ, and the velocity of sound that day. Was it a hot or a cold day ?