Quiz 2 (PHYS262, Summer 2001)

1

You are sitting inside a bus with a helium balloon hanging in the air. The density of helium in the balloon is less than that of air inside the bus. The bus is suddenly accelerated forwards. What happens to you and the balloon in the reference frame of the moving bus?

(a)

You are accelerated backwards, but the balloon is not accelerated in any way.

(b)

You are accelerated backwards, but the balloon is accelerated forwards.

(c)

You are accelerated forwards, but the balloon is accelerated backwards.

(d)

Both the balloon and you are accelerated forwards.

(e)

Both the balloon and you are accelerated backwards.

2

See Fig. 1. In the figure, a water tube is shown to have two ends with different cross-sectional area ($A_1$ and $A_2$ for left and right ends). Inside the tube, the water flows with velocities $v_1$ and $v_2$. For each of the two parts of the tube is an open-ended stand-pipe filled with water with height $h_1$ and $h_2$. At the open ends of the stand-pipe, the water is in contact with air with pressure $P_0$. In this situation, which of the following statements is FALSE? Assume that the density of water is $\rho$ and that water is an ideal fluid. Assume also that the velocity of fluid is zero at points $A$ and $B$.

Figure 1: Prob 2

(a)

The pressure difference between points $A$ and $B$ is $\rho g\vert h_1-h_2\vert$.

(b)

$A_1v_1 = A_2v_2$.

(c)

At point $C$, the pressure is $P_C = P_0+\rho g h_1 -{1\over 2}\rho v_1^2$. (Ignore the diameter of the tube compared to $h_1$ or $h_2$.)

(d)

If the pressure at points $C$ and $D$ are $P_C$ and $P_D$ respectively, $P_C+{1\over 2}\rho v_1^2 = P_D+{1\over 2}\rho v_2^2$. (Ignore the height difference between $C$ and $D$.)

(e)

None of the above.

3

Which one of the following waves can NOT sustain a transverse wave?

(a) Sound waves. (b) String waves. (c) Seismic waves (earthquake). (d) Slinkies. (e) Ripples on the surface of water.

4

A travelling wave is described by a function $y(x,t)$ in distance $x$ and time $t$, which only depends on an argument of the form $Ax+Bt$ with some coefficients $A, ~B$. The wave function is shown in Fig. 2a at a specific displacement $x=0$ from $t=0$ to $0.08 ~\rm sec$, and in Fig. 2b at a specific time $t=0$ from $x=0$ to $0.24 ~\rm m$. What is the magnitude and the direction of the velocity of this travelling wave? (Note: The scale of $y$ in Figs. 2a and 2b are different.)

Figure 2: Prob 4

(a)

$v=3 ~\rm m/s$, in the $x$ direction.

(b)

$v= 2 ~\rm m/s$, in the $x$ direction.

(c)

$v= 2 ~\rm m/s$, in the $-x$ direction.

(d)

$v= 0.5 ~\rm m/s$, in the $x$ direction.

(e)

$v= 0.5 ~\rm m/s$, in the $-x$ direction.

5

Which of the following statements is FALSE?

(a)

In sound waves, the pressure disturbance and the molecular displacement disturbance oscillate with the same phase.

(b)

If two or more travelling wave with small enough amplitudes are moving through a medium, the resultant wave function at any point is the algebraic sum of the wave functions of the individual waves.

(c)

Ideal springs with zero mass with a finite spring constant do not accommodate a travelling wave.

(d)

The velocity of travelling waves in the string or in the air is inversely proportional to the square root of the mass density of the medium.

(e)

All of the above.