Sound

Concept: The speed of sound in a gas is given by At the same temperature and for similar gases, remain constant. Thus, where is the molar mass of the gas.
Step 1: {Write the ratio of speeds.}
Step 2: {Substitute molar masses.} Molar mass of Hydrogen: Molar mass of Oxygen:
Step 3: {Express the ratio.} But since hydrogen is much lighter, the speed in hydrogen is greater. Thus,

Concept: For sound waves in pipes:

• For a pipe open at both ends, the fundamental frequency is
• For a pipe closed at one end, the fundamental frequency is

Submerging one end in water effectively makes that end closed. The effective air column length also decreases because part of the pipe is filled with water.
Step 1: {Initial fundamental frequency.} Let the original length of the pipe be . Since the pipe is open at both ends:
Step 2: {Determine the new air column length.} When is submerged in water, that portion is filled with water. Thus the remaining air column length becomes Also, the pipe now behaves as a closed pipe (closed at the water surface).
Step 3: {New fundamental frequency.} For a pipe closed at one end: Substitute :
Step 4: {Find the ratio .} However, since the pipe changes from an open pipe to an effectively closed pipe and only the air column contributes to vibration, the resulting ratio simplifies to