A sound wave propagates through a region filled with an ideal gas at constant temperature T. It approaches an acoustically permeable but thermally insulating membrane such that the angle between the wave and the plane of the membrane is 30 degrees. On the other side of the membrane is the same gas at a different temperature T. What is the minimum value of T/T such that no sound passes across the barrier? (You may find it useful to know that the speed of sound in an ideal gas is proportional to VT.) a.1 b.1/2 c.3/4 d.4/3. e.2.

We should make use of Snell's refractive law. The arriving wave has a certain velocity at T in a medium, then instantly it reaches a medium (same composition) at T' where velocity would either decrease or increase.

When the incidence angle is 30 °, and we want to make the refraction angle 90 ° such that no sound passes through the barrier (this would be named total internal refraction), so we want the second medium to be "faster" than in the first.

The steps are in the image attached: