This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Problems: WeekZ 2~1. A pendulum on Earth (g E : 9.8m/ 52) has a period of 1 see. What is its length? If you $3 take it to the moon what will its period be there if g M: ? If you want the period to be 1 sec on the moon by what factor must you change the length? 2—2. A spring—mass system is oscillating on a horizontal frictionless surface and its position‘is
given by x: 0.05 m cos wt. For what values of x will (i) its kinetic energy be maximum,
(ii) its potential energy be maximum (iii) its kinetic energy equal its potential energy, 23. If the system of problem 8—2 is hung from a ceiling, what will be the change in its ‘
frequency? Why? 25. 26. A wave on a stretched string is represented by
y = 0.01 sin(6.28.x ~ 12.560)? —> ‘ where distances are in meters and times in seconds. (i) Is this longitudinal or transverse? (ii) What is its wavelength, frequency, velocity? A sinusoidal wave of amplitude A and frequency a) , travelling on a stretched string
carries P=1A2w2£,where v: I
2 v ,u Joules of energy per second. Here T is the tension and v, the wave speed. Changing only one factor at a time how would P change if you
(i) double A (ii) halve a) or (iii) increase Tby a factor of 3. A sine wave y, = A, sin(kx + cut) is launched on one string with velocityy = :Egi. At
c x z 0, it encounters a second string where velocity is v' and gives rise to a reﬂected wave
y,. = A sinUrx — cut) and a transmitted wave y, f: A, sin(k'x + w't) . (i) What is the . .. . . A. ~
relatlon between a)’ anda) ? Why? (11) What determines k'? (111) leen that ~4— = v v i v+v‘ and i : 2v A  show that during reﬂection there is a phase change of H if v' << v.
, v + v 2—7. Using the result of problem 26 and the superposition principle, show that where the
A incident and reﬂected waves combine, nodes appear at x = 0,11301. =1,2,...) and
antinodes occur at x = (2n +1)—:1(n = 1,2,...) . 2—8. A wire of length 1m and mass 0.001kg has a tension of MN 111 it and is fixed at both
ends. Calculate the frequencies of the 3rd and 5th harmonic modes. 29. In the standing wave experiment that you have performed (a) why does the lowest (11 — 1)
mode require the largest tension (hanging mass)? (b) by what factor must you change the mass to get the 11 — 3 mode? ,
,, 210., The intensity of a periodic sound wave of amplitude s," and frequency a) in a gas at
pressure Po is ‘ P
I=lsmzw2 y 0
2 v S C . . .
Where y = E} and vs is the speed of sound. Calculate Sm for a1r1fP0=105N/m2, y = 1.4, v3: 330m/s and I: 10: lO'leatt/ m2; the quietest sound that can be heard. 2—11. A periodic sound wave can be thought of as a displacement wave
s = Sm sin(k;x — cut)
or a pressure wave
P=PD — Ps cos(kx—a)t) Why is the pressure ane always % out of phase with the displacement, that is, why is pressure variation maximum where displacement is zero and vice versa? 212. In air the speed of sound at room temperature is about 330m/s. What must be the
wavelengths of mechanical waves to be called sound? 2—13; The speed of sound in a gas is written as C
K. :JﬂfBT Where 7:4
Lm Cy .Why is there a “ 2/ ” in this equation? 2—14. Using the formula of 2—13 compare the speeds of sound in Helium [7 = 3m = 477119] and air [y = %,m ; 30mp]. 21 5. Compare the speed of sound in He (y = g) with the r.m.s. speed v atoms. "116' :51ch
m of He ...
View
Full Document
 Fall '11
 Bhagat
 Physics

Click to edit the document details